Difference between revisions of "Mean value theorem"
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| − | The '''Mean | + | 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: <math>f(b) - f(a) = f'(c)(b-a)</math>, where c is between b and a. | 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 18:21, January 3, 2009
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: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(b) - f(a) = f'(c)(b-a)} , where c is between b and a.