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So i got that the equation will be F=1000ft=4x+y and A=1/3xy
Is the river included as one side of the pens? cause in alot of problems it is..
you dont need fence for the river part
then we need 4x + y = 1000, right?
yea the 2 equations i set up are my up top
good, but I need to work it thru in my head too:)
take your time
and the area of each pen is x(y/3)
Since y = 1000 - 4x, can we use that in the area?
the deriviate and solve for max right?
esxucse typos, my keyboard hates me:)
no prob, yea
i get (3000 - 24x)/9 for a derivative...what about you?
hold on, did you set it up first by substituting?
x = 3000/24 = 1500/12 = 750/6..... yeah substitute in y=1000-4x.
so A(x)=1000x-4X^2 all over 3
x = 375/3...x = 125 for me
sorry im going slow
its ok...gives me time for my mind to wander :)
was my A(x) correct?
Your A(x) was correct...
then you took the derivative?
yep, the derivative tells us where we can find bends inthe graph that are our max and min values.
You remember your quotient rule?
yea let me do it one sec
3000-24x all over 9
yep; and theres another way we could have approached it. 1/3 is a constant so we can pull it out and just derivative (1000x-4x^2). Either way is the same
y did i get x=27000/24
solve for y' = 0. What makes (3000-24x)/9 = 0?
the top has to equal 0 for ay of it to matter; so throw away the 9
3000-24x = 0 what is x?
thats good too
1000 - 8x = 0...is the same thing
yep, now reduce it or use it as is if you want :) Good job
(500)(125)/3 is more accurate, but yeah...
20833ft^2, that seems large?
when talking about football field measurements, I imagine it would be :)
oh ok , now the other part is the maximum
2nd derivative right?
total inclosed area is 62500 ft^2
20833 1/3 each
they just want individual
so 20833ft^2 per pen
we already found the maximum... there is only one hump in a quadratic..
you can second derive it if you want, just to prove it to yourself, but it aint needed
i need to do all steps she takes off for everything
Is this 100% right, she had like inequality equations and domain stuff on her examples. I am confused
lol..when y'' is (+) we have a concave down which is an upside down bowl on the graph. And that is the max.
its right....so far :) use the math luke.....the maaatthhhh...
might wanna double check that concavity thing, I never use it enough to remember if Im right :)
it should be negative to be a max <0
remember CAVE....CAVE UP is (+) and CAVE DOWN is (-) or the other way around..
i mean in concavity relation
if its >0, its concave up oh okay
lol....ill trust you on that :)
how do you have a max then
picture the graph of (-x^2) thats all this is.
hold up is the second derivative -8
thats right, so the cave is down. its an upside down bowl.
-(x^2) ... y'=-(2x)....y'' = -(2)
oh i see
sorry, lol i am so bad at optimization
how do the domains work
she wants us to show that too D:(0, )
there is nothing limiting our domain, so it canbe any real number (R)
look at the fractions we made, if anything makes the bottom a 0, throw it out. Nothing matters, so keep it all
so (0, Infinity)
I suppose we should focus on positive numbers to make sense of it all, so yeah. except it should be [0,inf) 0 is included.
wait....just had athought
we only have so much fencing to work with... so make the D [0,1000]
or you might wanna think about like this: we need 4 amounts of x so ...maybe...[0,1000/4] ? take a gander at it and see :)
she likes simplicity
my gut tells me that we do [0,1000]..
my friend said the domain is 0 to 250
does your friend tell you how to find the max area :)
its your x
He said solve 1000x-4x^2 for x
and thats your A( )>0
which is your max by the Extreme value theorem
thats fine.....well use 0 to 250......its as good as anyother I can think of :)
no he said solve the inequality 1000-4x>0
thats what the 250 is
1000/4 = 250....i know iknow...yeahyeahyeah....
can we walk through it step by step, I am so confused
is 125 okay because it falls in the domain?
125 is good
step 1: we are given certian rules that govern our equations...did we use them right?
A'' in that case is <0 and negative which is why its a max?
we Know: 4x + y = 1000 and we KNow : Area per pen = xy/3
yes, since it is <0 it is a max
we want max area per pen so we substitute y in our area formula and get the derivative.
when y' = 0 we have a bend, a max OR a min.
which we just say is 1000-8x
yes.... and y'' tells us how the graph behaves at certain points. (-) = CAVE DOWN = max point (+) = CAVE UP = min point (0) = point of inflection.
so y''= -8
tells us it is always concave DOWN becasue its always (-8)
you still confused? or feeling more confident?
yea im getting it a little. He said since x fits in the open interval, you take the 2nd derivative
ahhhh where do I plug in our x in our second derivative?
why would you need to pluu it in? the only reason to plug in an x in the secondD is to figure out where is changes sign. -x^2 never changes concavity so it is always, and I mean ALWAYS cavedown
x^3 changes....so that youd check :) but we aint messin with no x^3
what is A'' of (1000x-4x^2)/3
lets see if it works anyway
A' = (1000-8x)/3 A'' = -8/3 A''' = 0
thats what i thought
you say this is calc 2 stuff?
cause im only in trig at the moment.....and it is sooooo boring there.
how are you helping me so well then?
i dunno, maybe I is smart ? I taught myself calculus in intermediate algebra to pass the time....
haha nice yea this is college calc 2
I still need alot of practice with integrals tho..... and word problems. I loathe word problems :)
yea you are still decent
Im gonna get my masters in math...and teach college math
i bet you can do it! easy 4 u
easy as....should I?......PI lol
thx so much though
no prob... keep up the good work :)
my friend confirmed everything