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AP Calculus AB· difficulty 2/5

A cube's edge length grows at 2 cm/s2~\text{cm/s}. When edge is 5 cm5~\text{cm}, its volume grows at

  • A

    150 cm3/s150~\text{cm}^3/\text{s}

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  • B

    30 cm3/s30~\text{cm}^3/\text{s}

  • C

    250 cm3/s250~\text{cm}^3/\text{s}

  • D

    50 cm3/s50~\text{cm}^3/\text{s}

Explanation

V=s3V = s^3, dV/dt=3s2 ds/dt=3(25)(2)=150 cm3/sdV/dt = 3s^2\,ds/dt = 3(25)(2) = 150~\text{cm}^3/\text{s}.

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