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Find the local max/min points for the function y=x^2 * e^x

  • calculus -

    by the product rule

    y' = x^2(e^x) + 2x(e^x)
    = e^x(x^2 + 2x) = 0 for max/min

    e^x = 0 ---> no solution or
    x^2 + 2x = 0
    x(x+2) = 0
    x = 0 or x = -2
    if x=0 then y 0
    if x = -2 then y = 4(e^2)

    so (0,0) and ( -2,4e^2) are max/min points.
    I will let you decide which is which.

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