AP Calculus BC 2.4 Differentiability Overview

Use limits and function behavior to explain why differentiability implies continuity and identify points where derivatives fail to exist.

Exam points

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36. If g is a differentiable function with g(1)=4 and $g^{\prime}(1)=3$ , which of the following statements could be false?

$\lim _{x \rightarrow 1^{+}} g(x)=\lim _{x \rightarrow 1^{-}} g(x)$

$\lim _{x \rightarrow 1} g^{\prime}(x)=3$

$\lim _{x \rightarrow 1} g(x)=4$

$\lim _{h \rightarrow 0} \frac{g(1+h)-g(1)}{h}=3$

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