Theorems
Mean Value Theorem
Also Known As Lagrange's Mean Value Theorem
Analysis
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The mean value theorem states that for a function continuous on a closed interval [a, b] and differentiable on the open interval (a, b), there exists some point c in (a, b) where the function's instantaneous rate of change equals its average rate of change over the whole interval.
Facts
StatementFor a function f continuous on [a, b] and differentiable on (a, b), there exists some c in (a, b) such that f prime of c equals f(b) minus f(a), divided by b minus a. 1 Cross-Tradition Connections
Sources
1. Mean Value Theorem (Wikipedia)
Wikimedia Foundationopening paragraphQuote, opening paragraph
the average rate of change of such a function over an interval is equal to the instantaneous rate of change at some point in the interval
1. Mean Value Theorem (Wikipedia)
Wikimedia FoundationStatement sectionQuote, Statement section
Let f : [a, b] to R be a continuous function on the closed interval [a, b], and differentiable on the open interval (a, b), where a < b. Then there exists some c in (a, b) such that f'(c) = (f(b) - f(a))/(b - a).
1. Mean Value Theorem (Wikipedia)
Wikimedia FoundationHistory sectionQuote, History section
The mean value theorem in its modern form was stated and proved by Augustin Louis Cauchy in 1823.
1. Mean Value Theorem (Wikipedia)
Wikimedia Foundationlead sectionQuote, lead section
the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions
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