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AP Calculus AB· difficulty 3/5

A rectangular open box with square base has surface area 4848. Find dimensions for maximum volume.

  • A

    Base 16\sqrt{16}, height 8\sqrt{8}

  • B

    Base 44, height 22

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  • C

    Base 424\sqrt 2, height 2/22/\sqrt 2

  • D

    Base 22, height 1111

Explanation

S=s2+4sh=48⇒h=(48−s2)/(4s)S = s^2 + 4 s h = 48 \Rightarrow h = (48 - s^2)/(4s). V=s2h=(48s−s3)/4V = s^2 h = (48 s - s^3)/4. V′=(48−3s2)/4=0⇒s=4,h=2V' = (48 - 3s^2)/4 = 0 \Rightarrow s = 4, h = 2.

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