(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the dimensions of a rectangular box with the largest volume with surface area 64cm^2.

2. Relevant equations

area of a rectangular prism 2xy+2yz+2xz

3. The attempt at a solution

took 2xy+2yz+2xz=64

rearranging for z:

z=(xy-32)/(y+x)

partial derivative of z with respect to x

y/(y+x)-(xy-32)/(y+x)^2

partial derivative of z with respect to y

x/(y+x) -(xy-32)/(y+x)^2

setting both derivatives equal to zero to obtain the critical point....

Here's where I hit a wall-

I cannot get a real root for y.

y/(y+x)-(xy-32)/(y+x)^2

y^2+xy=xy-32

y^2=-32

Please only help me up to this point until I ask you to help me further, I

want to challenge myself. Thank you!

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# Dimensions of box with largest volume

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