Rolle's Theorem: A Special Case of the Mean Value Theorem

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question 1 of 3

According to Rolle's theorem, for a continuous function f(x), if the start point f(a) and the end point f(b) equal 0 then:

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1. Consider the function f(x) given below. According to Rolle's theorem, for how many values of x is the instantaneous rate of change equal to 0?

2. Consider the function f(x) given below. According to Rolle's theorem, between x=0 and x=pi, for how many values of x is the instantaneous rate of change equal to 0?

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About This Quiz & Worksheet

After taking a look at what Rolle's theorem states about the measure of change of a projectile's path, this quiz and corresponding worksheet will help you gauge your knowledge of this theory. Topics you'll need to know to pass the quiz include understanding what Rolle's theorem is as well as how to find the instantaneous rate of change.

Quiz & Worksheet Goals

Use this printable worksheet and quiz to review:

  • Rolle's theorem problems
  • Continuous functions

Skills Practiced

This worksheet and quiz will let you practice the following skills:

  • Interpreting information - verify you can read information regarding how to find the instantaneous rate of change and interpret it correctly
  • Reading comprehension - ensure that you draw the most important information from the related Rolle's theorem lesson
  • Problem solving - use acquired knowledge to solve Rolle's theorem problems

Additional Learning

To learn more about why something going up must come back down, review the corresponding Rolle's Theorem lesson. This lesson will help you:

  • Understand what Rolle's theorem is
  • Describe the relationship of Rolle's theorem and the average value theorem
  • Identify the equation for the theorem
  • Explain how to find the instantaneous rate of change
  • Appreciate when the rate of change equals zero on a graph
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