2
$\begingroup$

I have the function $f(x) = a x e^{1+ax}$ and I want to find where it has a min or max value.

To do this I calculate the derivative f'(x) = a^{2}x e^{1+ax}. This is equal to $0$ only if $a=0$ or $x=0$.

How to proceed from here?

  • 0
    @AndréNicolas Holy! I better go sleep now. Now I realized that I am really tired.2011-12-08

1 Answers 1

0

Since $f$ is only a function of $x$, we will take $a$ to be constant (unless it's a function of $x$, in which case you need to specify that).

Using the product rule, f'(x)=ae^{1+ax}+a^2xe^{1+ax}=ae^{1+ax}(1+ax). From here, I think you can find the critical point of $f$.

  • 0
    Hint:to determine if the critical point is$a$global minimizer, maximizer, or neither, determine where $f$ is increasing and where $f$ is decreasing.2012-06-08