Hey, I was just reviewing all the tests for tmmrws GRE exam and I cant seem to find the correct answer for problem #63.

f(x) = xe^(-x^2 - x^-2) for x!= 0

and 0 for x=0

How many horizontal tangent lines are there for f(x)?

a) None

b) One

c) Two

d) Three

e) Four

Answer: D (I guessed c)

I found f' and I can only seem to get two values for when the derivative is 0. Can anyone tell me where the third is?

EDIT: I'm guessing its because as x approaches 0 the derivative approaches 0. Missed this :/, should have expected something like that since it isnt defined at 0 (at least for the derivative).