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Math Help - Maxima & Minima

  1. #1
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    Maxima & Minima

    1) g(x) = x^2(e^-x)
    (Give exact values for the coordinates of any maxima or minima. Use 3-decimal-place accuracy for inflection-point coordinates.)

    -I differentiated g(x) and got g'(x)= x^2(-e^-x) + (e^-x(2x)). I am not sure how to continue the problem and am a little confused with the algebra involved. If any one knows how to do this problem, please help me. Thank you.
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  2. #2
    Junior Member
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    have:

    g = x^2 e^{-x}

    and you differentiated wrt x to get:

    g' = 2xe^{-x} - x^2e^{-x}

    we want to set the derivative to zero:

     0 = (2x - x^2) e^{-x}

    well the exponential function is never zero for x in reals so:

    0 = x(2-x)

    we have x=0 \text{ or } x=2 and then calculate higher derivatives of g to find the nature of these turning points.
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