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Curve Sketching

AP Calculus AB· difficulty 3/5

A function with f(0)=0f(0) = 0, ff increasing on (0,∞)(0, \infty), and concave down everywhere on (0,∞)(0, \infty) — could be

  • A

    f(x)=−xf(x) = -x

  • B

    f(x)=xf(x) = \sqrt x

    check_circle
  • C

    f(x)=xf(x) = x

  • D

    f(x)=x2f(x) = x^2

Explanation

x\sqrt x: increases, concave down (since f′′=−14x−3/2<0f'' = -\tfrac{1}{4}x^{-3/2} < 0).

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