AP Calculus AB Mean Value Theorem and Extreme Value Theorem Quiz: 10 Questions with Explanations

AP Calculus AB math quiz: Mean Value Theorem and Extreme Value Theorem – Maths PDF

Cover of the book AP Calculus AB Math Tests with Answer Keys (PDF)

Download as a PDFThe AP Calculus AB tests book with answer keysPrintable PDFSee the book ›

Sommaire

This mvt evt quiz for AP Calculus AB covers mean value theorem and extreme value theorem (Common Core AP CALC AB 5.1, AP CALC AB 5.2, AP CALC AB 5.3), with a free PDF to print.

Test yourself on the Mean Value Theorem, the Extreme Value Theorem, critical numbers and absolute extrema on closed intervals with 10 multiple-choice questions. Pick one answer for each question, then read the explanation to see why it is right and which common mistake the other choices represent.

AP Calculus AB · Common Core State Standards: AP CALC AB 5.1, AP CALC AB 5.2, AP CALC AB 5.3

Mvt evt quiz: 10 questions

Question 1

Which condition is NOT required by the Mean Value Theorem?

Question 2

For \(f(x)=x^{2}\) on \([0,6]\), what is the value \(c\) from the MVT?

Question 3

Secant and tangent.

The secant of \(y=x^{2}\) on \([0,4]\) has slope 4. At which \(x\) is the tangent parallel to it?

Question 4

Why can’t the MVT be applied to \(f(x)=|x|\) on \([-2,2]\)?

Question 5

What is a critical number of \(f(x)=x^{2}-6x\)?

Question 6

Graph of f(x) = x³ − 3x.

How many critical numbers does \(f(x)=x^{3}-3x\) have?

Question 7

What is the absolute maximum of \(f(x)=x^{2}-4x\) on \([0,5]\)?

Question 8

Which theorem guarantees an absolute maximum for a continuous function on \([a,b]\)?

Question 9

Values of f at the candidates.

From the candidates table, what is the absolute minimum value of \(f\) on \([0,4]\)?

Question 10

A car’s average speed over a 3-hour trip is 55 mph. What does the MVT guarantee?

Remember

MVT: f′(c) = (f(b) – f(a))/(b – a) for some c in (a, b), if f is continuous and differentiable.
EVT: a continuous function on a closed interval has an absolute maximum and an absolute minimum.
Critical numbers are where f′ = 0 or f′ is undefined (inside the domain).
Candidates test: compare f at endpoints and critical numbers.

How to use this mvt evt quiz

Answer each question, read the explanation that appears, and keep track of your score. A score of 8 out of 10 or more means you are ready for the test.

Download the mvt evt quiz as a PDF with the button below and keep it with your notes.

All AP Calculus AB chapters: AP Calculus AB math.

Voter.. post

Free printable PDF