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

For the function $f(x)=x^3-3x^2+2$, the second derivative is $f''(x)=6x-6$. What does the Second Derivative Test say about the point where $f'(x)=0$ and $x=2$?

Question 2

Which statement best describes the Second Derivative Test for a critical point $x=c$?

Question 3

Suppose $f'(a)=0$ and $f''(a)=0$. What can be concluded from the Second Derivative Test?

Question 4

For $f(x)=x^2+4x+1$, what type of extremum occurs at the critical point?

Question 5

A function has a critical point at $x=5$ and satisfies $f''(5)<0$. What is the most likely conclusion?