how to find the dimensions of the rectangular box having the largest volume and surface area 150 square units?
I was afraid you'd say that.
The max volume for a closed box with a fixed surface area will be a cube.
Here is the work ...
let x , y , and z be the length, width, and height.
since
since ...
set both partials = 0 ...
combine both equations ...
since ...
the "cube"