instantaneous rate of change?

Question

Let f(x)= e^(x^2). At how many points in the interval [-a, a] does the instantaneous rate of change of f equal the average rate of change of f?
a. none
b. one
c. two
d. three
e. more than three

Answer 1

The average rate of change over {-a,a} would be [f(a)-f(-a)]/2a. But f(a) = f(-a), so the average rate of change is 0. The instantaneous rate of change is df(x)/dx = 2xe^(x^2); This is zero at x = 0 only. So I would say there is one point that meets the criterion.

Answer 2

I believe none...