5. Analytical Applications of Differentiation

Using The Candidates Test To Determine Absolute (global) Extrema — Quiz

Test your understanding of using the candidates test to determine absolute (global) extrema with 5 practice questions.

Practice Questions

Question 1

What is the main idea of the Candidates Test for finding an absolute maximum or minimum on a closed interval $[a,b]$?

Question 2

Why must the endpoints be included when using the Candidates Test on a closed interval $[a,b]$?

Question 3

A function has critical points at $x=1$ and $x=4$ on the interval $[0,5]$. Which set of $x$-values should be checked in the Candidates Test?

Question 4

Suppose $f(0)=3$, $f(2)=7$, and $f(5)=5$ are the only candidate values on $[0,5]$. What is the absolute maximum value of $f$ on $[0,5]$?

Question 5

A function is continuous on $[a,b]$. What theorem helps justify that an absolute maximum and an absolute minimum must exist on that interval?