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AP Calculus AB· difficulty 3/5

The legs of a right triangle change: a=4a = 4 m and growing at 1 m/s1~\text{m/s}, b=3b = 3 m and shrinking at 0.5 m/s0.5~\text{m/s}. The area changes at

  • A

    2 m2/s2~\text{m}^2/\text{s}

  • B

    1 m2/s1~\text{m}^2/\text{s}

  • C

    0.5 m2/s0.5~\text{m}^2/\text{s}

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  • D

    0 m2/s0~\text{m}^2/\text{s}

Explanation

A=ab/2A = ab/2, dA/dt=(a′b+ab′)/2=((1)(3)+(4)(−0.5))/2=(3−2)/2=0.5dA/dt = (a' b + a b')/2 = ((1)(3) + (4)(-0.5))/2 = (3 - 2)/2 = 0.5.

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