Set up and evaluate the optimization problem.

Question

To carry a suitcase on an airplane, the length + width + height of the box must be less than or equal to 74 in. Assuming the height is fixed, verify that the maximum volume is V = h(37-(1/2)h)^2. What height (in inches) allows you to have the largest volume?

Answer 1

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Deteremine first derivative of V

Set V'(h) = 0