Optimization

AP Calculus AB· difficulty 3/5

A closed rectangular box has square base. With volume 32 m332~\text{m}^3, minimize the surface area. The base side and height that minimize are

  • A

    Base 22, height 88

  • B

    Base 44, height 22

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  • C

    Base 88, height 0.50.5

  • D

    Base 1616, height 1/81/8

Explanation

S=2s2+4shS = 2 s^2 + 4 s h with s2h=32s^2 h = 32. Substituting and minimizing yields s=4,h=2s = 4, h = 2.

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