# Math Help - Local Maximum Problem

1. ## Local Maximum Problem

Find constants a and b in the function f(x)=axe^(bx) such that f(1/3)=1 and the function has a local maximum at x=1/3.
Thanks!

2. Originally Posted by iheartthemusic29
Find constants a and b in the function f(x)=axe^(bx) such that f(1/3)=1 and the function has a local maximum at x=1/3.
Thanks!
Solve the following simultaneously:

$1 = \frac{a}{3} e^{b/3}$ .... (1)

$f'(1/3) = 0 \Rightarrow a e^{b/3} + \frac{ab}{3} e^{b/3} = 0$ .... (2)

3. I figured it out.
a=3e and b=-3
Thanks!