# Difference between revisions of "Mean Value Theorem"

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In words, there is a number <math>c</math> in <math>(a,b)</math> such that <math>f(c)</math> equals the average value of the function in the interval <math>[a,b]</math>. | In words, there is a number <math>c</math> in <math>(a,b)</math> such that <math>f(c)</math> equals the average value of the function in the interval <math>[a,b]</math>. | ||

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+ | ==Proof== | ||

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+ | ==Other== | ||

Rolle's Theorem is a sub-case of this theorem. It states that if <math>f(a)=f(b)=0</math> for two real numbers a and b, then there is a real number c such that <math>a<c<b</math> and <math>f'(c)=0</math>. | Rolle's Theorem is a sub-case of this theorem. It states that if <math>f(a)=f(b)=0</math> for two real numbers a and b, then there is a real number c such that <math>a<c<b</math> and <math>f'(c)=0</math>. |

## Revision as of 11:27, 7 August 2018

The **Mean Value Theorem** states that if are real numbers and the function is differentiable on the interval , then there exists a value in such that

In words, there is a number in such that equals the average value of the function in the interval .

*This article is a stub. Help us out by expanding it.*

## Proof

## Other

Rolle's Theorem is a sub-case of this theorem. It states that if for two real numbers a and b, then there is a real number c such that and .

*This article is a stub. Help us out by expanding it.*