AP®︎ Calculus AB: Topic 2.4 Practice Test
Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 2.4 of AP Calculus AB – Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist.
Questions List
Topic 2.4
Question 1 Easy
If is differentiable at , which of the following must be true?
What You’re Being Tested On:
Explore the learning objectives taken directly from the College Board’s AP® Calculus AB Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.
Topic 2.4: Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist (domain of f')
Learning Objective: FUN-2.A
Explain the relationship between differentiability and continuity.
Essential Knowledge: FUN-2.A.1
If a function is differentiable at a point, then it is continuous at that point. In particular, if a point is not in the domain of f, then it is not in the domain of f'.
Essential Knowledge: FUN-2.A.2
A continuous function may fail to be differentiable at a point in its domain. Illustrative examples: The left hand and right hand limits of the difference quotient are not equal, as in f(x) = |x| at x = 0. The tangent line is vertical and has no slope, as in f(x) = x^(1/3) at x = 0.
