Science:Math Exam Resources/Courses/MATH110/April 2012/Question 03 (a)
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Question 03 (a) 

State either the Mean Value Theorem or Rolle's Theorem. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

What conditions need to be true for the function for Rolle's Theorem / the Mean Value Theorem to be true? 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Let be continuous on an interval and differentiable on . Mean Value Theorem: Then there exists a c in (a,b) such that Rolle's Theorem: In addition to the conditions of continuity and differentiability, if , then there exists a c in (a,b) such that . 