Calculus

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For the function g(x) = xe power x, there is inflection point at?

  • Calculus -

    g(x) = xe^x
    g'(x) = xe^x + e^x
    g''(x) = xe^x + e^x + e^x
    = e^x( x+2)

    at point of inflection g''(x) = 0
    so e^x = 0 ----> no solution
    or x+2 = 0
    x = -2
    then g(-2) = -2e^-2 or -2/e^2

    point of inflection (-2, -2/e^2)

  • Calculus -

    The average value of f(x) = e ^ 4xsquared on the interval [-1/4,1/4]

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