5. Analytical Applications of Differentiation

Using The Second Derivative Test To Determine Extrema — Quiz

Test your understanding of using the second derivative test to determine extrema with 5 practice questions.

Practice Questions

Question 1

If $f'(c)=0$ and $f''(c)>0$, what can be concluded about $f$ at $x=c$?

Question 2

Suppose $f'(c)=0$ and $f''(c)<0$. What does the Second Derivative Test say about $f$ at $x=c$?

Question 3

For which situation does the Second Derivative Test fail to give a conclusion?

Question 4

A function $f$ has $f'(c)=0$ and $f''(c)=4$. What is the most likely behavior of $f$ near $x=c$?

Question 5

Let $f'(c)=0$ and $f''(c)=-2$. Which statement is correct?