help with optimization! (attached)

- anonymous

help with optimization! (attached)

- jamiebookeater

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- anonymous

##### 1 Attachment

- anonymous

okay i understand everything..... except how to find the minimum!

- anonymous

are you familiar with derivative?

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## More answers

- anonymous

i know they got the equation. y=6x+(21000/x)

- anonymous

yes

- anonymous

then after i'm not sure how they got: Minimum occurs at 59.16 ft for the length (found on a graphing calc) width: 10500/59.16 = 177.5 ft Perimeter = 710 ft

- anonymous

ok, well the method they got the minimum is just by using a graphing calculator with a max min function on it doing it manually would involve finding the first derivative of the equation and then setting it equal to zero and then solving for L

- anonymous

or x

- anonymous

is there a way to do that without it?

- anonymous

without the graphing calculator? or without having to do it manually?

- anonymous

by hand

- anonymous

no calculator

- anonymous

by hand would involve finding the first derivative of the equation and then setting it equal to zero and then solving for L

- anonymous

because the slope at the minimum point is zero

- anonymous

can you show me?

- anonymous

im doing it wrong, even on calculator :/ I'm not getting it.

- anonymous

\[y = \frac{21000}{x} + 6x\] \[y' = -\frac{21000}{x^2} +6\] \[y' =0\] \[0=-\frac{21000}{x^2} +6\] solve for x hopefully i didnt screw up the derivative

- anonymous

\[\frac{1}{x} = x^{-1}\]

- anonymous

any questions?

- Psymon

@completeidiot derivative is fine :3

- anonymous

yeah 1/x?

- anonymous

im just pointing out the identity that allows you to use the "power" rule for derivatives

- anonymous

\[y= x^n\] \[y' = nx^{n-1}\]

- anonymous

im not getting that. i got up to here: y=6-21000/x^2 then set it to 0

- anonymous

then im lost

- anonymous

1/x is not part of the problem you can ignore it if you want its just that the identity is sometimes not obvious to other people

- anonymous

once you set it equal to zero 0=6-21000/x^2 just solve for x

- anonymous

6= 21000/x^2 x^2= 21000/6 x = sqrt {21000/6}

- anonymous

any other questions? sorry for any confusion i may have caused

- anonymous

i got it=]

- anonymous

thanks!

- anonymous

no problem

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