jessica
  • jessica
Find the minimum distance between the curves y=-x^2 and y=(6-x)^2
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
bahrom7893
  • bahrom7893
WOOT MY FAVE TOPIC! OPTIMIZATION!
bahrom7893
  • bahrom7893
let me refresh my memory real quick.
jessica
  • jessica
so glad you can help i've been stuck for like 2 hours.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

bahrom7893
  • bahrom7893
what was the distance formula again? sorry haven't done this in almost 2 years
bahrom7893
  • bahrom7893
nevermind ill get one of my review books
bahrom7893
  • bahrom7893
k workin on it
jessica
  • jessica
sorry the distance formula is \[D= \sqrt{(x1-x2) ^{2}+(y1-y2)^{2}}\]
bahrom7893
  • bahrom7893
okay well how far did u get in this problem? I've never done problems with curves. Only distance to the point. Do u have anoy worked out examples?
bahrom7893
  • bahrom7893
I mean the problems i used to solve were find the minimum from curve to a point
jessica
  • jessica
Right that's where I'm having the problem so I've created a formula by subtracting the two curves from eachother... hold on i'll put all my work on here, i thought i had gotten to an answer, but my answer didn't make sense so now i'm back at square 1
bahrom7893
  • bahrom7893
k
jessica
  • jessica
Let D(x) = | [(6 – x)^2] - [-x^2] | be the function representing the Distance between those two given functions. Both of the given functions are continuous. So D(x) is continuous. If D(x) is 0 at some point, then that’s our minimal distance. Otherwise, D(x) is never zero. And so it would be always strictly positive or strictly negative for any x. Can it ever be true that those two curves cross, making D(x) = 0? We’d like to solve –x^2 = (6-x)^2. This gives –x^2 = 36 – 12x + x^2. Or x^2 – 6x + 18 = 0. This yields only complex roots, and so the curves never cross for any x. Therefore, either D(x) is always negative, or it is always positive. (It can’t go between being positive and negative or else it would have to be zero at some point.) Let’s pick a test point, some easy point to evaluate D(x). Like D(0). D(0) = 36. So D(x) will always be positive. Moreover, we want to minimize D(x), and we can drop the absolute value bars now. [If D(x) was always negative, we would then want to maximize D(x) to find the minimal distance (I don’t know if that makes sense to you).] So minimize it using calculus. Find the critical points of D’(x). Then test to see whether those critical points are minima (x = c is a minimum if f’(c) = 0 (or x = c is a cusp) and f’(x) < 0 for x slightly less than c and f’(x) > 0 for x slightly bigger than c). Then choose the smallest minimum. (I think there’s only one minimum in this case.)
jessica
  • jessica
I found my minimum to be x=3 but then i didn't know if that three needed to be plugged into the original equations, and then the distance found between those two points. That didn't make sense becuase the points were (3,9) and (3,-9) and the distance from that is way far
bahrom7893
  • bahrom7893
im getting x = 3 too
jessica
  • jessica
Does that thought process make sense though? What does the 3 mean... Do I just find D(3)? 18 doesn't seem like the right answer
jessica
  • jessica
Look at the graphs of those 2 equations and you'll see what why it doesn't make sense
bahrom7893
  • bahrom7893
k brb lemme find my calculator
bahrom7893
  • bahrom7893
the minimum is 1.5
bahrom7893
  • bahrom7893
wait no
jessica
  • jessica
how did you get that answer?
bahrom7893
  • bahrom7893
nevermind i just looked at the graph and my first guess was 1.5, but then if u move up along one and down the other u'll see that there are maybe closer point
bahrom7893
  • bahrom7893
what class is this?
jessica
  • jessica
multivariable calc
jessica
  • jessica
my teacher is ridiculous. we've never been over anything like this... and i have no idea what i am doing.
bahrom7893
  • bahrom7893
im checkin the stuff, i think i gotta get my other textbook, i took calc 3 last semester.. worst class ever.
jessica
  • jessica
it's been better then linear algebra if you ask me... just wish i had a better teacher
jessica
  • jessica
i actually have to go to a meeting, and i'll be back in like an hour... but i really really appreciate any help that you could throw out there for me
jessica
  • jessica
sorry to peace like this
bahrom7893
  • bahrom7893
okay where can i send the stuff to?
jessica
  • jessica
you could put it on here, or email me at vballninja@gmail.com
bahrom7893
  • bahrom7893
k
jessica
  • jessica
thanks so much!!!!!
bahrom7893
  • bahrom7893
np, ill do my best
bahrom7893
  • bahrom7893
i found some stuff, looking thru it
bahrom7893
  • bahrom7893
we were differentiatin it wrong
jessica
  • jessica
how are we supposed to differentiate it?
bahrom7893
  • bahrom7893
http://in.answers.yahoo.com/question/index?qid=20100218090950AAGvf4z see there it's like we need first to find derivative with respect to x1 then x2
bahrom7893
  • bahrom7893
hey can u go on twiddla? it'll be easier to write there i think
bahrom7893
  • bahrom7893
http://www.twiddla.com/494934
bahrom7893
  • bahrom7893
hey jessica click on the link above, im waitin for u on twiddla
bahrom7893
  • bahrom7893
ill wait here too just in case
jessica
  • jessica
sorry i'm in the meeting now so i'm like trying to be discrete
bahrom7893
  • bahrom7893
oh okay, fine then just wait till its over, i got plenty of time right now

Looking for something else?

Not the answer you are looking for? Search for more explanations.