Extreme Value Theorem & Bolzano's Theorem


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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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1. If a function is continuous on the closed interval from x = 1 to x = 3, what does the extreme value theorem tell you about the function?

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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About This Quiz & Worksheet

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

Additional Learning

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