Determining Concavity

AP Calculus AB· difficulty 2/5

For f(x)=ex2f(x) = e^{-x^2} (Gaussian), ff'' at x=0x = 0 is

  • A

    Positive

  • B

    Zero

  • C

    Cannot determine

  • D

    Negative

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Explanation

ff has a maximum at x=0x = 0 (bell curve peak), so concave down there → f(0)<0f''(0) < 0.

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