I am working on a mix/max problem and am stuck.

$\displaystyle y=xe^(-\frac{x^2}{8})$ within the interval of [-1,4]. The exponent of e is $\displaystyle -\frac{x^2}{8}$, can't get Latex to cooperate with me.

Using the product rule to differentiate and I get:

y'= $\displaystyle e^(-\frac{x^2}{8})+x(e^(-\frac{x^2}{8})(\frac{x}{4})$

Factor out the $\displaystyle e^(-\frac{x^2}{8}$ and I get

$\displaystyle e^(-\frac{x^2}{8})(1+\frac{x^2}{4})$

For all real numbers, the 2nd term will never equal 0, so the only one that can equal 0 is $\displaystyle e^(-\frac{x^2}{8})$.

I don't know how to solve for x when $\displaystyle e^(-\frac{x^2}{8})=0$. Any pointers?