What are the critical points and also inflection points of #3e^(-2x(^2))#?
Assuming that the function is:
The only critical number is
# = -12e^(-2x^2)(1-12x^2)#
#f''(x) is never undefined, so the only chance it has to change signs is when it is zero.
Observe that the sign of
The inflection points are:
(Simplify and rationalize if you prefer.)