Difference between revisions of "Mean Value Theorem"
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− | The ''' | + | The '''Mean Value Theorem''' states that if <math>a < b</math> are [[real number]]s and the [[function]] <math>f:[a,b] \to \mathbb{R}</math> is [[continuous]] on the [[interval]] <math>[a,b]</math>, then there exists a value <math>c</math> in <math>[a,b]</math> such that |
− | <cmath>f(c)=\dfrac{1}{b-a}\int_{a}^{b}f(x)dx</cmath> | + | <cmath>f(c)=\dfrac{1}{b-a}\int_{a}^{b}f(x)dx.</cmath> |
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>. |
Revision as of 15:10, 17 July 2008
The Mean Value Theorem states that if are real numbers and the function
is continuous 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
.
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