1. (10 points) Let f(x) be defined in a neighborhood of the origin. Show that if f'(0) exists, then $$\lim_{h \to 0} \frac{f(h) - f(-h)}{2h} = f'(0).$$ Give a counter example to show that the converse is not true in general, that is, if the above limit exists, then it is not necessary that $f'(0)$ exists.