AP®︎ Calculus BC: Topic 5.2 Practice Test
Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 5.2 of AP Calculus BC – Extreme Value Theorem, Global Versus Local Extrema, and Critical Points.
Questions List
Topic 5.2
Question 1 Easy
The graph of on the closed interval is shown. What is the absolute maximum value of on ?
What You’re Being Tested On:
Explore the learning objectives taken directly from the College Board’s AP® Calculus BC 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 5.2: Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
Learning Objective: FUN-1.C
Justify conclusions about functions by applying the Extreme Value Theorem.
Essential Knowledge: FUN-1.C.1
If a function f is continuous over the interval ( a, b ) , then the Extreme Value Theorem guarantees that f has at least one minimum value and at least one maximum value on [ a, b ] .
Essential Knowledge: FUN-1.C.2
A point on a function where the first derivative equals zero or fails to exist is a critical point of the function.
Essential Knowledge: FUN-1.C.3
All local (relative) extrema occur at critical points of a function, though not all critical points are local extrema.
