# Math Help - Maxima & Minima

1. ## 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.

2. 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.