Math

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Find the absolute extrema of

f(x)= (2x-1)e^(-x) on [0, 00)

  • Math -

    f ' (x) = (2x-1) e^(-x) ( -1) + 2 e^(-x)
    = 0 for a max/min

    e^(-x) (2 - (2x-1)) = 0
    e^(-x) ( 3 - 2x) = 0
    e^(-x) = 0 ----> no solution
    or
    3 - 2x = 0
    x = 3/2
    then f(3/2) = 2e^(-3/2) = 2/e^(3/2)

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