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 a critical point of a function $f$?

Question 2

What does the Extreme Value Theorem guarantee if $f$ is continuous on $[a,b]$?

Question 3

A function has an absolute maximum at $x=5$ with value $12$. What does this mean?

Question 4

For $f(x)=x^2-4x+3$, what is the critical point?

Question 5

For $f(x)=|x|$, which point is a critical point?