# Math Help - Functions and Points

1. ## Functions and Points

For the function $y=c(e^{-at} - e^{-bt})$

With a,b,c > 0 and t ≥ 0 find the point at which y reaches its maximum.

I have:

$f' (t) = c (-ae^{-at} + be^{-bt})$

...and then i'm stuck

2. Let the derivative equal zero and solve for t.
$0 = c (-ae^{-at} + be^{-bt})$
So
$0 = -ae^{-at} + be^{-bt}$

Can you show
$e^{(a-b)t}=\frac{a}{b}?$

If so, solve for t.