# Solving derivative of exponential function

1. Nov 17, 2009

### synergix

1. The problem statement, all variables and given/known data
-Find the intervals on which f is increasing or decreasing
-Find the local maximum and minimum values of f
-Find the intervals of concavity and the inflection points
f(x)=xex
f'(x)= ex+xex
then I must solve for x when the function equals zero to find my critical numbers
2x+ln(x)=0

3. The attempt at a solution

The problem is I dont know how to get rid of the ln() to solve for x. Not that it would help all my terms have x's. so how would I find the critical number of this function? or is their only one, zero? zero because ln()is undefined at zero

2. Nov 18, 2009

### clamtrox

This tells you where the logarithm of the derivative is zero, which is not what you were asked for. Instead try

$$f'(x) = (1+x)e^x = 0$$ if $$e^x = 0$$ or ...

3. Nov 21, 2009

### synergix

x1=-1
If I try and solve e^x for zero i get x DNE so how do I find out where the critical point is?

4. Nov 21, 2009

### synergix

or is -1 the only critical number?

5. Nov 21, 2009

### Bohrok

Yes, x = -1 is the only critical point since ex is never 0.

6. Nov 21, 2009

thank you