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?
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?
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 $f$.