# Homework Help: Intervals of increase/decrease with a exponential function

1. Jun 16, 2006

### endeavor

find the intervals of increase and decrease of f(x) = e3x + e-2x.

f'(x) = 3e3x - 2e-2x
I set f'(x) = 0 to find the critical numbers:
3e3x = 2e-2x
3 ln e3x = 2 ln e-2x
9x = -4x
x = 0, which is obviously wrong, (3e^0 - 2e^0 = 1). I found out that I had to combine the two terms using a common denomintor, and I got the right answer.

But why did my original method fail?

2. Jun 16, 2006

### Hootenanny

Staff Emeritus
Quite simply because;
$$3\ln|e^{3x}| \neq \ln |3e^{3x}|$$

3. Jun 16, 2006

### endeavor

ahh.... i feel so stupid.. i hate when i make simple mistakes and mix formulas up. :uhh:

4. Jun 16, 2006

### Hootenanny

Staff Emeritus
I did a very similar thing in an exam yesterday, I was sat there for fifteen mintues trying to figure out where I had gone wrong, then I realised, I had differentiated instead of integrated , it was a good job I realised before the end of the test!