I think you are computing the height wrongly:
2(32/xy) + 2(32/x) + 2(32/y) SHOULD BE
2(xy) + 2(32/x) + 2(32/y)
Please try again.
A closed rectangular box has a volume of 32 cm^3. What are the lengths of the edges giving a minimum surface area?
I came up with an equation for surface area:
2(32/xy) + 2(32/x) + 2(32/y) with x and y being the length and width of the edges and height solved in terms of x and y so I just have two variables.
Next, I got my f sub x and f sub y and set them equal to zero to obtain a global min. I must be doing something crazy because I keep getting only a negative value for x which is equal to y at -1 which is wrong. The answer is 32^(1/3) but I sure can not get this. Any help on where I went wrong would be much appreciated. Frostking