(New page: My favorite theorem is La grange's Mean Value Theorem . I like it because its quite simple but has many far fetched applications and is one of the most fundamental theorems of calculus. Th...) |
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<math>f'(c)=\frac{f(b)-f(a)}{b-a}</math>. | <math>f'(c)=\frac{f(b)-f(a)}{b-a}</math>. | ||
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| + | Rolle's theorem is a special case of this theorem. | ||
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| + | More information about when it was first described and its applications can be found [http://en.wikipedia.org/wiki/Mean_value_theorem here] and also [http://www.artofproblemsolving.com/Wiki/index.php/Lagrange%27s_Mean_Value_Theorem here] . | ||
Latest revision as of 19:37, 28 August 2008
My favorite theorem is La grange's Mean Value Theorem . I like it because its quite simple but has many far fetched applications and is one of the most fundamental theorems of calculus. The theorem states that:
Let $ f(x) $ be a function of x subject to:
a. $ f(x) $ is a continuos function of x in the closed interval $ a<=z<=b $. b. $ f'(x) $ exists for every point in the open interval a<x<b, then there exists at least one value of x, say c such that $ a<c<b $ where $ f'(c)=\frac{f(b)-f(a)}{b-a} $.
Rolle's theorem is a special case of this theorem.
More information about when it was first described and its applications can be found here and also here .
