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Determining Concavity

AP Calculus AB· difficulty 2/5

f(x)=cos⁡xf(x) = \cos x is concave up where

  • A

    sin⁡x>0\sin x > 0

  • B

    x>0x > 0

  • C

    sin⁡x<0\sin x < 0

  • D

    cos⁡x<0\cos x < 0

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Explanation

f′′(x)=−cos⁡x>0⇔cos⁡x<0f''(x) = -\cos x > 0 \Leftrightarrow \cos x < 0.

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