Math Questions and Answers

Start Your Free Trial

`f(x) = e^(2x) + e^(-x)` (a) Find the intervals on which `f` is increasing or decreasing. (b) Find the local maximum and minimum values of `f`. (c) Find the intervals of concavity and the inflection points.

Expert Answers info

Luca B. eNotes educator | Certified Educator

calendarEducator since 2011

write5,348 answers

starTop subjects are Math, Science, and Business

You need to determine where the function increases or decreases, hence, you need to verify where f'(x)>0 or f'(x)<0.

You need to determine derivative of the function:

`f'(x) = 2e^(2x) - e^(-x)`

Putting f'(x) = 0, yields:

`2e^(2x) - e^(-x) = 0`

`2e^(2x) - 1/(e^x) = 0 => 2e^(3x) - 1 = 0 => e^(3x) = 1/2 => e^x = root(3)(1/2)`

`x = ln...

(The entire section contains 196 words.)

Unlock This Answer Now

check Approved by eNotes Editorial