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    Optimization for trapezoid

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    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 Preview

    See attachment please!

    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.


    Solution Summary

    This shows how to find the cross section of maximum area for a given solid.