AP Calculus BC 2.4: Differentiability and Continuity

Practise AP Calculus BC 2.4 by deciding when differentiability guarantees continuity and using limits or difference quotients to justify conclusions at a point.

Exam points

Use continuity and differentiability implications to decide which statements must hold at a point.
Interpret limits and difference quotients to identify where a function is not differentiable.

[Maximum number: 1]

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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FUN-2.A—Explain the relationship between differentiability and continuity question 1