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AP Calculus AB 2.4 Connecting Differentiability and Continuity Question Bank

Practise AP Calculus AB 2.4 questions by connecting continuity with derivative existence in graphs and piecewise formulas.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • distinguish continuity from differentiability using limits, corners and cusps
  • use one-sided derivative behaviour to test piecewise differentiability

Covered syllabus points

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

2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist question 1

[Maximum number: 1]

If f(x)={x2 for x≤12x−1 for x>1f(x)=\left\{\begin{array}{ll}x^{2} & \text { for } x \leq 1 \\ 2 x-1 & \text { for } x>1\end{array}\right., then

A

f(x) is not continuous at x=1

B

f(x) is continuous at x=1 but f′(1)f^{\prime}(1) does not exist

C

f′(1)=2f^{\prime}(1)=2

D

lim⁡x→1f(x)\lim _{x \rightarrow 1} f(x) does not exist

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