AP Calculus BC 2.4 Connecting Differentiability and Continuity Determining When Derivatives Do and Do Not Exist Questions

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

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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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