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anonymous
 5 years ago
Using Lagrange multipliers to find the maxium and minimum values of the function f(x,y,z)+xy^2z^3 subject to x^2+y^2+2z^2=25. PLEASE HELP
anonymous
 5 years ago
Using Lagrange multipliers to find the maxium and minimum values of the function f(x,y,z)+xy^2z^3 subject to x^2+y^2+2z^2=25. PLEASE HELP

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So you're gonna go through the equation taking derivatives with respect to all three variables but one at a time. So first, derive the equation with respect to the variable 'x' while treating y,z like constants, that's one derivative. Then do the same again but with only y as the variable, and then again with z.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Let me know when you have done that much!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so I need to take partials in respect to each variable fx, fy, fz?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so fx=y^2z^3 fy=2xyz^3 fz=3xy^2z^2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, partials. gimme a second

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wait a second, rephrase your question. what do you mean by f(x,y,z)+xy^2z^3 ??

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you have two functions?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0f(x,y,z)=xy^2z^3 subject to the constraint of x^2+y^2+2z^2=25

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'm in the middle of two other quesitons. If you're not rushed, I can get back to you on this one. alright?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0not rushed it is due in the morning, thank you for your help. this site is fun

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i couldn't get thru, som' about about the server not receiving my post but I'm still looking at the problem. Just grabbed my snack and I'm not browsing my calc book.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it's an optimization. very much in the line of those classic optimization problems in simpler calculus but I haven't done one in a bit

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i am confused because i left my book at home and I am at school

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0something to do with taking the gradient of the constraint

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we have not done this type of problem, and i have no information in my notes

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which calculus are you taking?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0calc 4, 3d vectors, multivarible

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0problem is only worth 5 points but i think it is important to know how to do it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i'm dining and browsing pages at the same time...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0in a weird way, i miss school; funny how that works

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0eat, i dont want to ruin your dinner, just get back to me when you are finished

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i only have 2 more math classes and 3 physical chem classes and 3 chem engineering classes and then I am done

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lol, then heading for the petroleum industry?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i want to do desalinization, water filtration, water is the next oil!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0or if i could figure out how to make coal a clean fuel source

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the chapter on lagrange multipliers starts: in my applications we must find the extrema of a function of several variables when the variables are restricted in some manner.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0f (xyz) =xyz + (2xz + 4yz + 8xy − C) does this formula seem familiar

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you're end up with 2 numbers at the end, the maximum and minimum.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0correct this is what i need

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i need to solve for x and y

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0correct? i could be wrong

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0actually, it's a little different

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0z is negilble because it is the depth and not going to be a min or a maxium

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the minimum and maximum values will be points on the graph which happens to be a 3 variable function

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0all the variables are going to count

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the maximum and minimum values will be points in a 3 dimensional space, so they'll look like (x1,y1,z1) and (x2,y2,z2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if we didn't have the constraint, it would be straight forward. we'd find the partials, set them all equal to zero and then solve for the three variables.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0since we would have fx=0, fy=0, fz=0; all equations in their own right, and we have 3 variables, we would be able to solve this problem completely.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0depending on how many CRITICAL points we find, some could be maximum(s) and others minimum(s)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so take the partials and set them equal to zero and solve for a x, y, or z and plug the values into the equations

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is that the first step?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that would only be if we didn't have a constraint; since we have a constraint, we need to find a way to include it in our optimization.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so take the constraint and solve for one of the variables. pick which ever one you'd like

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0by the way, i take it you're in college...what year?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the contratint is x^2+y^2+2z^2=25

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and let me know once you have solved for one of the variables in the constraint...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that's correct. chose one variable, x, y or z and solve for it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I graduated from Stanford and I'm currently working in the DC area

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0chose a variable that's gonna make it easy on you cuz we'll have to plug whatever that variable is equal to into the f(x,y,z) function!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0once we do that, we'll have one function with only 2 variables and we can find the two partials, set them equal to zero and solve!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0show me your work and let me know what you're thinking so that I can guide you in case you get lost...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0with the 2 present in the constraint the value i get solving for x=5y\sqrt{2z ^{2}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[x=5y\sqrt{2z ^{2}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you! much better

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0walk me thru how you got this step by step...or just to the part before you took the square root

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the constraint equation is \[x ^{2}+y ^{2}+2z ^{2}=25\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0solve for X, so I squared both sides

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0first you took y^2 and 2z^2 to the other side

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, then squared both sides

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and then you had \[x^2 = 25  2z^2  y^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the square of the right isn't exactly what you got bradley

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so should i not square the equation?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay so what do i do with it? do i plug it into the partial?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the square root of 252z^2y^2 doesn't simplify to that.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0dude, give 10 minutes

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh how i hate contraints

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes it does simplft to that

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i'm back and we're gonna solve this problem. sorry for the delay

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i need to find a gradient of the the f(x,y,z) right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, but we need to take the constraint into account

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so we solve for one variable, x like you did above

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the \[x= \sqrt{252z^2y^2} \neq 5  y  \sqrt{2x2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the \[x=\sqrt{252z^2y^2} \neq 5  y  \sqrt{2x^2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if you're not sure why those two are NOT equal, look it up when you get a chance.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i figured that part out

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now back to our function, plug this new found value of x into our original function replacing it at every place where x shows up

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay i already did that

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the original function was \[f(x,y,z) = xy^2z^3\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0here's another thing to think about: if you had chosen y instead of x, we would be square it and getting rid of the nasty square root. you wanna do that again?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do let me know what you're thinking and if you're start getting lost...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\sqrt{252z ^{2}y ^{2}}y ^{2}z ^{3}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh did not think of that

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but you see why that would have been smart?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0why does the y solve and the radical go away?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh never mind i see it, let me check

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Bradley, we're solving this without using Lagrange Multipliers (LMs)....this is gonna give us another but apparently the LMs provides a nicer way....we're gonna look into that after.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it's very good to see you check your work and see why things are why they are. keep it up!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0once you have the function of \[f(x,z)\] you can find fx and fz, set them equal to zero and solve them. you'll have 2 equations and 2 variables. you see why it's gonna fx and fz? because why will have been replaced by those two.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[x(252z ^{2}x ^{2})z ^{3}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what is this? always remember to represent functions in terms of f(x)=something...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0in this case it would be \[f(x)=....\]. multiply it out and then find fx and then fz.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so what i wrote before is the f(x,z)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now can you find fx and fz, set them equal to zero and solve for x and z?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so take the partial of each?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0note: this will give you the answer, but not using the method the suggested. i'm looking at exactly how Lagrange Multipliers work. it's something like \[\Delta f(x,y,z) = \lambda \Delta g(x,y,z)\] where \[g(x,y,z)\] will be your constraint function.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0partial of fx=\[25z ^{3}2z ^{5}xx ^{3}z ^{3}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the Lagrange multiplier is no jok but we might be able to figure out if you stick around :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0fz=\[75xz ^{2}10z ^{4}x3x ^{3}z ^{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i am here until it is done

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0damn, these are some nasty looking numbers!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0nasty looking functions i should say

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yep, i think this is why the lagrange multiplers are needed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0any way, let's finish this first. if we can, lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so we set those partials to zero and see what happens

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0are you good with algebra?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that's what I like to hear! so let's simply the hell out of these two and solve the system of 2 equations to find the solution

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so set them both equal to zero, simplify, and then solve for x and z

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let me know if you get stuck

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i see alot of quadratic forumla in my future

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we might break half way and make the jump to langrage...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0there are multiple variables so i can do the quadatic, even after factoring out some things

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you think it would be better to take the graident of f(x,z)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0might be a little easier but not much easier. i'm looking at a \[5x^33x^250\] for this one

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0a calculator might solve it...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0where does that come from?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[f _{x}=25z^32z^5xx^3z^3=0 => f_{x}=252z^2xx^3\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[f_{z}=75xz^210z^4x3x^3z^2=0 => f_{z}=7510z^23x^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the last part was \[3x^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if you solve that, eliminate \[z\] by multiplying the first with 5 and adding both equations you get what i got.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0check my work, i may have made an algebraic error while I double check this langrage business

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0at the very least, you'll have an answer for this question and then we can worry about the method.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i am not seeing the x^3 is coming from

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no when i added the 2 i got 12x^2  50

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0in the fx why did you not factor out z^3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I did. look at the part after the => sign

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0am I missing something here? plz do let me know, I could have easily made a mistake...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0btw, I admire your persistence. I know you could say the same for me but I enjoy this kind of thing. Usually I enjoy working on challenging and interesting problems, but I didn't when I was a student. I did, but I didn't put in the work. so good job thus far.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0by the way, I have a problem here in my book which is a superb example for solving this problem with lagrange multipliers. I don't have a scan, but I can take a pic with my camera. so if you'd like you can send your email so i can forward it to you.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lets start with the basics f(x,z)=\[25xz^32z^5xx^3z^3\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0brower.brad@gmail.com

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0fx=\[25z^32z^53x^2z^3\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0fx=\[z^3(252z^23x^2)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0btw, what you typed in earlier: f (xyz) =xyz + (2xz + 4yz + 8xy − C) does this formula seem familiar. this is what we'll end up referring back to for the langrage.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0was that in your notes somewhere?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0fz=\[75xz^210z^4x3x^3z^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that was from a volume equation the variables were off, dont think it matters

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0fz=\[xz^2(7510z^23x^2)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i see the problem in the book but i guess i am having trouble seeing what to do with what i find

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so you have the example to a similar problem as well that is being solved using Lagrange Multipliers?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0by the way, the x^3 came from the original fx that you gave me. I didn't check it. if it was true, that's where the x^3 was coming from.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0must have been a type, there shouldn't be a x^3. just checked.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea, so it should nicely reduce then

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so then it is x=\[\sqrt{50}/12\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0by adding5 to fx and adding to fz the z^2 canceled

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right, but now you plug the value of x into one of them to solve for z as well. remember?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorrying multiply 5 to fx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so plug in the \[5\sqrt{2}/12\] to the orignal functions

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0maybe i am doing poor algebra, wait do i plug it into f(x,y,z) or f(x,z)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[f_{x}=252z^23x^2\] and \[f_{z}=7510z^23x^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\sqrt{50}/12(252z^2(\sqrt{50}/12)^2)z^3\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0subtract those two: \[f_{z}f_{x} = 508z^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that's right. now plug that into either fx or fz

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so if i plugged the z value into fx, i would solve for X?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what do you have for me?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you realize that once you get the x we'll now have x and z, and remember the expression of y you got earlier by solving for y? well, if you go and plug this x and z in it, you'll have the y which will give you a point in 3D (x,y,z) and that will be the solution!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I just got through looking at the Lagrange and it is considerably easier once you get it. let me know when you're ready to move on.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the x is difficult because of the fractions

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It's nearing 11 o'clock my time, so we'll have to hurry up a bit :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0awww, not a fan of fractions are ya? no worries

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0just teasin' by the way,

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i agree i am about done

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so let's figure out this fraction business

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[f_{x,z=5/2}=252(5/2)^23x^2x\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0simplying gives us: \[0=2525/23x^2=50/225/23x^3\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.050/225/2=25/2, right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0because you get (5025)/2=25/2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so we now have \[25/23x^2=0 => 25/2=3x^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you can get x from there

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry my brain is fried the whole thing must be squared

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0don't worry, that makes two of us

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which simplifies to...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, but by convention you don't leave a radical in the bottom so you...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0multiply both top and both by the same radical and you get...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now, if we didn't make any stupid mistakes along the way, those two should be two of the 3 you need to make a point in 3D

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now plug all three into the equation

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now plug those into the y expression you got earlier and you should get the third point to form (x,y,z)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0once you have the point, that's it. that should be the optimal point you were looking for to satisfy whatever the problem was asking you to satisfy in real life

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now onto lagrange: given \[f(x,y,z)\], and the constraint \[x^2+y^2+2z^2=25\], let \[g(x,y,z)=x^2+y^2+2z^225\]. Now, all the wise Lagrange himself said was that given that the gradient of \[g(x,y,z\] neve equals zero, there exist a constant such that the gradient of \[f(x,y,z)\] equals the constant times the gradient of \[g(x,y,z)\].

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0first, you know now how you're gonna get the y?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and at least have your optimal point? before we do this now. we're just gonna quickly set up the equations and I'm gonna hit the pellets

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah y=\[\sqrt{25/3}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sweet. i haven't checked it. make sure all the algebra's right.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0go ahead and go to sleep i appreciate all your help, it was above the call of duty

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you see how I wrote the constraint as the function g(x,y,z) ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so langrage gives you a bunch of easy equations to solve: here they are:

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0he says that there exists a constant, \[lambda\] that when multiplied by the constraint, you get the solution. interesting man

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so here are the equations: fx = lambda*gx, fy = lambda*gy, fz = lambda*gz, and finally, we have our constraint: g(x)=0;

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lambda as I am using it here is of course \[\lambda\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0with the g(x,y,z)=0 we have 4 equations which is great because we have 4 variables: x,y,z, and \[\lambda\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so take the partial of gx, gy, gz and solve for lambda

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that is exactly correct! of course you'll also be taking partials of fx,fy,and fz but remember that here we're talking about the original \[f(x,y,z)=xy^2z3\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes! awesome, i got it! thank you so much for your help

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0in the process you'll solve for the lambda, x,y, and z. you're interested in the x,y,and z and if we did everything right, they should match what we got earlier.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i understand it know thanks so much

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0good to know where everything comes from

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0or that there are easier ways of getting things done :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if i ever get stuck can i email you?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you're welcome. you have my email, shoot me one if you ever need some more help. i don't visit here often.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you beat me to it; absolutely.
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