Question

Critical Points & Inflection Points of

f(x) = e^x-2e^(-x)-3x

Answer 1

You know what to do here?

Answer 2

I know that the critical point comes from the 1rst deriv and 2nd deriv gives the inflection point but I'm messing up somewhere :/

Answer 3

You're on the right track! Let's first get the expression for the 1st derivative.
Would you like to work this derivative?

Answer 4

e^x+2e^(-x)-3

Answer 5

Yep! :)

Answer 6

To find the critical points (CP), we set this derivative = 0 and solve for x.

Answer 7

\[e ^{x} \space + 2e ^{-x} \space -3 = 0\]

Answer 8

Do you have an idea how to go about solving this equation for x ?

Answer 9

Good or awful idea to try to ln it?

Answer 10

This won't work unfortunately! :(

Answer 11

There's actually a "trick" required to solve this equation...

Answer 12

Okay yeah I'm kind of lost then!

Answer 13

Obviously can just toss the -3 over

Answer 14

let's first multiply through by e^x