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Extrema: First Derivative Test

AP Calculus AB· difficulty 3/5

For f(x)=ex−xf(x) = e^x - x, ff is increasing on

  • A

    (−∞,0)(-\infty, 0)

  • B

    (−∞,∞)(-\infty, \infty)

  • C

    (0,∞)(0, \infty)

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  • D

    (1,∞)(1, \infty)

Explanation

f′(x)=ex−1>0f'(x) = e^x - 1 > 0 for x>0x > 0. (And f′<0f' < 0 for x<0x < 0.)

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