Rolle's Theorem: Difference between revisions
New page: '''Rolle's theorem'' is an important theorem among the class of results regarding the value of the derivative on an interval. ==Statement== Let <math>f:[a,b]\rightarrow\mathbb{R}</math> L... |
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==Statement== | ==Statement== | ||
Let <math>f:[a,b]\rightarrow\mathbb{R}</math> | Let <math>f:[a,b]\rightarrow\mathbb{R}</math> | ||
Let <math>f</math> be continous on <math>[a,b]</math> and differentiable on <math>(a,b)</math> | Let <math>f</math> be continous on <math>[a,b]</math> and differentiable on <math>(a,b)</math> | ||
Let <math>f(a)=f(b)</math> | Let <math>f(a)=f(b)</math> | ||
Then <math>\exists</math> <math>c\in (a,b)</math> such that <math>f'(c)=0</math> | Then <math>\exists</math> <math>c\in (a,b)</math> such that <math>f'(c)=0</math> | ||
Revision as of 20:15, 14 February 2008
'Rolle's theorem is an important theorem among the class of results regarding the value of the derivative on an interval.
Statement
Let ![$f:[a,b]\rightarrow\mathbb{R}$](http://latex.artofproblemsolving.com/6/7/c/67c320754a36aaec178e61f04bfcbac41c0bf675.png)
Let 
be continous on ![$[a,b]$](http://latex.artofproblemsolving.com/8/e/c/8ecbd1ba3da8f2adef66a63f2ab32c47e63fa734.png)
and differentiable on 
Let 
Then 
such that 
