Solving derivative of exponential function

[synergix]

Homework Statement

-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)=xe^x
f'(x)= e^x+xe^x
then I must solve for x when the function equals zero to find my critical numbers
2x+ln(x)=0

The Attempt at a Solution

The problem is I don't 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

 

[clamtrox]

2x+ln(x)=0

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 ...

 

[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?

 

[synergix]

or is -1 the only critical number?

 

[Bohrok]

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

 

[synergix]

thank you