Difference between revisions of "Mean value theorem"
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| − | The '''Mean Value Theorem''' of [[Calculus]] states that for some value ''c'' on the [[function]] ''f'' on some interval [a, b], ''f'(c)'' (the [[slope]] of ''f'' at ''c'') will equal the average slope over [a, b]. | + | The '''Mean Value Theorem''' of [[Calculus]] states that for some value ''c'' on the [[function]] ''f'' on some interval [a, b], ''f'(c)'' (the [[slope]] of ''f'' at ''c'') will equal the average slope over [a, b], provided that ''f'' is continuous over the interval [a, b] and differentiable on the interval (a, b). |
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| + | This is written algebraically as: <math>f(b) - f(a) = f'(c)(b-a)</math>, where c is between b and a. | ||
[[Category:Mathematics]][[category:calculus]] | [[Category:Mathematics]][[category:calculus]] | ||
Revision as of 02:57, December 12, 2008
The Mean Value Theorem of Calculus states that for some value c on the function f on some interval [a, b], f'(c) (the slope of f at c) will equal the average slope over [a, b], provided that f is continuous over the interval [a, b] and differentiable on the interval (a, b).
This is written algebraically as: , where c is between b and a.
