# Extreme Value Theorem & Bolzano's Theorem

Instructions:

Choose an answer and hit 'next'. You will receive your score and answers at the end.

question 1 of 3

### If a function changes from negative to positive in the closed interval between x = 2 and x = 3, which of the following could be a solution to the function according to Bolzano's theorem?

Create Your Account To Take This Quiz

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-free for 30 days. Cancel anytime.

### 2. A continuous function stays positive on the interval x = 4 to x = 6. What does Bolzano's theorem tell you about this function?

Create your account to access this entire worksheet
A Premium account gives you access to all lesson, practice exams, quizzes & worksheets
Quizzes, practice exams & worksheets
Certificate of Completion
Create an account to get started

Both the extreme value theorem and Bolzano's theorem will be examined in this combination of a quiz and worksheet. You will be asked about solutions that supply the rules of each theorem, and perform practice problems with both theorems, as well.

## Quiz & Worksheet Goals

Expect to find the following topics on the quiz and worksheet combo:

• Solutions with Bolzano's theorem
• Using the extreme value theorem
• Continuous functions and Bolzano's theorem
• Finding a minimum

## Skills Practiced

• Problem solving - use what you have learned to solve problems using both theorems
• Knowledge application - utilize what you know of the theorems to answer questions about continuous theorems
• Information recall - remember what you have studied about changing negative to positive

For more review, visit the lesson titled, Extreme Value Theorem & Bolzano's Theorem. There, you can find the following subjects:

• Graphs of functions
• Minimums and maximums
• Sine and cosine functions
Final Exam AP Calculus BC: Exam Prep
Status: Not Started
Chapter Exam Function Continuity
Status: Not Started

Support