Originally Posted by

**adamsmurmur** Alright, here's my first attempt. I sort of understand what I have to do, but I'm not clear on how to properly show it.

Let the symmetric derivative of f at x be,

lim h->0 (f(x+h) + f(x-h) - 2f(x))/(h)

Prove that there exists a point x in the open interval (0,1).

Note that (f(x+h)+ f(x-h)- 2f(x))/h= f(x+h)- f(x))/h + f(x-h)- f(x))/h

Looking at one-sided limits,

Let L = f(x+h)- f(x))/h. Then, the lim h -> 0- f(x+h)- f(x))/h >= 0. As h approaches 0 from the left, the limit must be greater than or equal to zero.