Question

Find the dimension of a rectangular parallelepiped with fixed total edge length with maximum surface area

Answer 1

Answer:

your procedure is correct if not for the slight differential errors in dzdxanddzdy which has, in turn, resulted in all the wrong values. I followed your procedure, and these are the expressions and values I get for the differentials

Zx=−(k+y2)(x+y)2Zxx=2(k+y2)(x+y)3Zxy=2(k−xy)(x+y)3Zy=−(k+x2)(x+y)2Zyy=2(k+x2)(x+y)3

using these the double differential values of function V that you get will be

Vxx=−aVyy=−aVxy=−a/2

I have ommitted writing the expressions for these as they were pretty long