ap-calculus-ab None Q6

ap-calculus-ab · Usa · -bc_sample-questions Differentiation from First Principles

Let $f$ be the piecewise-linear function defined by $$f ( x ) = \begin{cases} 2 x - 2 & \text { for } x < 3 \\ 2 x - 4 & \text { for } x \geq 3 \end{cases}$$ Which of the following statements are true? I. $\lim _ { h \rightarrow 0 ^ { - } } \frac { f ( 3 + h ) - f ( 3 ) } { h } = 2$ II. $\lim _ { h \rightarrow 0 ^ { + } } \frac { f ( 3 + h ) - f ( 3 ) } { h } = 2$ III. $f ^ { \prime } ( 3 ) = 2$
(A) None
(B) II only
(C) I and II only
(D) I, II, and III

Let $f$ be the piecewise-linear function defined by
$$f ( x ) = \begin{cases} 2 x - 2 & \text { for } x < 3 \\ 2 x - 4 & \text { for } x \geq 3 \end{cases}$$
Which of the following statements are true?\\
I. $\lim _ { h \rightarrow 0 ^ { - } } \frac { f ( 3 + h ) - f ( 3 ) } { h } = 2$\\
II. $\lim _ { h \rightarrow 0 ^ { + } } \frac { f ( 3 + h ) - f ( 3 ) } { h } = 2$\\
III. $f ^ { \prime } ( 3 ) = 2$\\
(A) None\\
(B) II only\\
(C) I and II only\\
(D) I, II, and III

Paper Questions

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