A trough with trapezoidal cross sections is formed by turning up the edges of a 30 inch wide sheet of aluminum. Find the cross section of maximum area.
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Solution. Denote the area of the cross section by S. Then we have
Obviously, is a function with two variables such that .
Now we are going to find its maximum. First, we need to find the partial derivatives.
This shows how to find the cross section of maximum area for a given solid.