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Extrema: First Derivative Test

AP Calculus AB· difficulty 2/5

For f(x)=x2e−xf(x) = x^2 e^{-x} (x>0x > 0), ff is decreasing where

  • A

    x>2x > 2

    check_circle
  • B

    x<1x < 1

  • C

    x>1x > 1

  • D

    x>0x > 0

Explanation

f′(x)=2xe−x−x2e−x=xe−x(2−x)f'(x) = 2x e^{-x} - x^2 e^{-x} = x e^{-x}(2 - x). For x>2x > 2, f′<0f' < 0.

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