I know you have to find the derivative first which I got:

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

f'(x)= (-2e^-x)+(4e^-2x)

But now, how do I go about finding one of the x? I believe you must rewrite it as a quadratic function but since the exponent is -2 indicating it is a reciprocal.

So:

(4(e^x)^-2)-(2(e^x)^-1)=0

Factoring: Divided by 4

(1/e^x)((1/e^x)-(1/2))=0

I can set ((1/e^x)-(1/2))=0 which will be x = ln 2

But when it comes to (1/e^x)=0 I'm at a COMPLETE LOSS. How do I do this?

Thank you in advance