5. Analytical Applications of Differentiation

Using The First Derivative Test To Determine Relative (local) Extrema — Quiz

Test your understanding of using the first derivative test to determine relative (local) extrema with 5 practice questions.

Practice Questions

Question 1

What does the First Derivative Test use to determine whether a critical point is a relative maximum, relative minimum, or neither?

Question 2

Suppose $f'(x)$ changes from positive to negative as $x$ passes through $x = c$. What happens at $x = c$?

Question 3

A critical point occurs at $x = c$, and $f'(x)$ is negative on both sides of $c$. What can be concluded?

Question 4

For $f(x) = x^2$, what is the relative extremum at $x = 0$?

Question 5

If $f'(x)$ changes from negative to positive at a critical point, which statement is correct?