# Extreme Value Theorem & Bolzano's Theorem Video

Instructions:

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?

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

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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