AP Calculus AB Increasing, Decreasing and the First Derivative Test Quiz: 10 Questions with Explanations

AP Calculus AB math quiz: Increasing, Decreasing and the First Derivative Test – Maths PDF

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This first derivative quiz for AP Calculus AB covers increasing, decreasing and the first derivative test (Common Core AP CALC AB 5.4, AP CALC AB 5.5, AP CALC AB 5.6), with a free PDF to print.

Test yourself on increasing and decreasing intervals, sign charts of the derivative, the First Derivative Test and absolute extrema 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 5.4, AP CALC AB 5.5, AP CALC AB 5.6

First derivative quiz: 10 questions

Question 1

If \(f^{\prime}(x) < 0\) on an interval, then \(f\) is

Question 2

Sign chart of f′.

What does \(f\) have at \(x=2\)?

Question 3

For \(f(x)=x^{3}\), what happens at the critical number \(x=0\)?

Question 4

Where is \(f(x)=x^{2}-4x\) increasing?

Question 5

The graph of f′.

The graph shows \(f^{\prime}\). At which \(x\) does \(f\) have a relative maximum?

Question 6

If \(f^{\prime}\) changes from positive to negative at \(x=c\), then \(f\) has

Question 7

What is the relative minimum of \(f(x)=x\ln x\)?

Question 8

Signs of f′.

According to the table, where does \(f\) have a relative maximum?

Question 9

Which statement is true?

Question 10

For \(f^{\prime}(x)=(x-1)^{2}(x+2)\), which critical number is a relative minimum?

Remember

A positive f′ means f is increasing; a negative f′ means f is decreasing.
Sign changes of f′ can occur only at critical numbers or where f′ is undefined.
First Derivative Test: + to − gives a relative maximum; − to + gives a relative minimum.
A critical number without a sign change, such as x = 0 for x³, is not an extremum.

How to use this first derivative 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.

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