Critical Points & Inflection Points of

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

Question

Critical Points & Inflection Points of 

f(x) = e^x-2e^(-x)-3x

miracrown · Answer

You know what to do here?

anonymous · Answer

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

miracrown · Answer

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

anonymous · Answer

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

miracrown · Answer

Yep! :)

miracrown · Answer

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

miracrown · Answer

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

miracrown · Answer

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

anonymous · Answer

Good or awful idea to try to ln it?

miracrown · Answer

This won't work unfortunately! :(

miracrown · Answer

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

anonymous · Answer

Okay yeah I'm kind of lost then!

anonymous · Answer

Obviously can just toss the -3 over

miracrown · Answer

let's first multiply through by e^x

miracrown · Answer

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