5. Analytical Applications of Differentiation

Extreme Value Theorem, Global Versus Local Extrema, And Critical Points — Quiz

Test your understanding of extreme value theorem, global versus local extrema, and critical points with 5 practice questions.

Practice Questions

Question 1

Which statement best describes the Extreme Value Theorem?

Question 2

A function has a local maximum at $x=c$. What must be true near $x=c$?

Question 3

Which of the following is a critical point of a differentiable function $f$?

Question 4

A continuous function $f$ is defined on the closed interval $[1,4]$. Where should you look to find its absolute maximum and absolute minimum values?

Question 5

A function has a local minimum at $x=2$. Which statement must be true?