define and prove rolles theorem

define and prove rolles theorem


1 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
9 years ago

212-1580_Rolles theorem.png

If areal-valued functionfiscontinuouson aclosed interval[a,b],differentiableon theopen interval(a,b), andf(a)=f(b), then there exists acin the open interval (a,b) such that df(x)/dx at x=c is zero.


It can be claimed, since the function is continuous and its value at end points is equal, so it must attains a maximum in between at some point c, which imply that its derviative should be zero at that point.

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