
Maxima & Minima
1) g(x) = x^2(e^x)
(Give exact values for the coordinates of any maxima or minima. Use 3decimalplace accuracy for inflectionpoint 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.

have:
$\displaystyle g = x^2 e^{x}$
and you differentiated wrt x to get:
$\displaystyle g' = 2xe^{x}  x^2e^{x}$
we want to set the derivative to zero:
$\displaystyle 0 = (2x  x^2) e^{x} $
well the exponential function is never zero for x in reals so:
$\displaystyle 0 = x(2x)$
we have $\displaystyle x=0 \text{ or } x=2$ and then calculate higher derivatives of $\displaystyle g$ to find the nature of these turning points.