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

MATH110 April 2012

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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 $f$ for Rolle's Theorem / the Mean Value Theorem to be true?

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. Let $f(x)$ be continuous on an interval $[a,b]$ and differentiable on $(a,b)$. Mean Value Theorem: Then there exists a c in (a,b) such that $\displaystyle f'(c)={\frac {f(b)-f(a)}{b-a}}$ Rolle's Theorem: In addition to the conditions of continuity and differentiability, if $f(a)=f(b)$, then there exists a c in (a,b) such that $f'(c)=0$.

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