Moderate# Derivative of Piecewise Function, Given Its Graph

APCALC-EAYELZ

Consider the piecewise linear function $f(x)$ whose graph is shown below.

Which of the following is equivalent to $f'(2)$?

I.$\lim \limits_{x \to 2} \cfrac{f(x)-f(2)}{x-2}$

II.$\lim \limits_{h \to 0} \cfrac{f(2+h)-f(2)}{h}$

III.$\lim \limits_{h \to 0} \cfrac{f(2+h)-f(2-h)}{2h}$

IV.$2$