I didn't learn how to do this in my class, and the examples in my book do not apply to this type of problem.
To make a rectangular trough, you bend the sides of a 32-inch wide sheet of metal to obtain the cross section pictured below. Find the dimensions of the cross section with the maximum area. (this will result in the trough with the largest possible volume).
I don't really know how to proceed. I know that I need to use derivatives to solve this, but I can't seem to get started
Best Answer
Hint: let $h$ be the height of each side and $w$ be the width of the bottom. Can you write an equation based on the width of the strip? Can you write one for the area of the cross section? Solve the first for one variable, plug it into the second, and you will have an equation for the area that depends upon one variable. Take the derivative, set to zero....