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 say about a function at a point where $f'(x)$ changes from positive to negative?

Question 2

A function is increasing on $(-\infty,2)$ and decreasing on $(2,\infty)$. What is the relative behavior at $x=2$?

Question 3

Suppose $f'(x)$ changes from negative to positive at $x=c$. What can be concluded?

Question 4

Which situation shows that the First Derivative Test gives no relative extremum at $x=c$?

Question 5

For $f(x)=x^2-4x+1$, at what $x$-value does the First Derivative Test show a relative extremum?