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AP® Calculus AB-BC

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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. $2$

A

I and II only.

B

I, II, and III only.

C

I, II, and IV only.

D

I, II, III, and IV.