Solve "Derivative Problem: Find Min & Max of (e^(-x)) - (e^(-2x))

[Eshi]

Homework Statement

I have to find the min and max of this function using derivatives:

(e^(-x)) - (e^(-2x))

The Attempt at a Solution

f'(x) = -e^(-x) + 2x(e^(-2x))
So now i set that to zero, and I get...

2x(e^(-2x)) = e^(-x)

And at this point I have no idea what to do. If you divide e^-x by e^-2x can u do something with the exponents?

 

[jeffreydk]

Double check your derivative, you shouldn't be bringing an x down right? The derivative of e^cx for a constant c is just ce^cx

 

[Eshi]

o i ggot it! so it become

2 = e^(-x-2x)
and then you simply take the ln...

thanks jeffreydk

 

[jeffreydk]

No problem.

Watch out though, I think you have a sign error in there.

f'(x)=-e^-x+2e^-2x=0

So then 2e^-2x=e^-x

and therefore by dividing you get 2=e^-x+2x