The truck is a rectangular box open at the top. Let be the length and be the width; then the depth is . The surface area is .
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For minimum (clearly it won't be a maximum here),
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Here also, an immediate solution is , so that , for minimum, and
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Exercises XV. (See page 262 for Answers.)
(1) Differentiate the expression with respect to alone, and with respect to alone.
(2) Find the partial differential coefficients with respect to , and , of the expression
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(3) Let .
Find the value of . Also find the value of .
(4) Find the total differential of .