Problem:Find values ofaandbso that the function has a local maximum at the point (6, 18).

$\displaystyle f(x) = axe^{bx}$

How do I solve this? Could you show your steps so I can see what you're doing and why? Also, how do you solve it to be a local maximum or minimum? I don't understand the concept of this problem at all, much less this specific problem.

EDIT: I found the value of b by taking the derivative of the original equation, which is:

$\displaystyle f\prime(x) = ae^{bx}(1 + bx)$

Then I solved for a:

$\displaystyle a = \frac{18}{e^{6b}(1 + 6b)}$

I plugged that back into the original derivative, set it equal to 0, and solved for b, getting $\displaystyle \frac{-1}{6}$, which is correct.

However, I can't figure out how to solve for a now! I keep getting an answer of 0, which I know isn't right!