what is rolles theorem

what is rolles theorem


1 Answers

Spandan Pratyush, IIT Delhi
14 Points
13 years ago

Dear Nithin,

Rolles theorem says that, if for a continous and differentiable function f, f(a)=f(b), then f'(c)=0, atleast for one c lying between a and b.

That means graphically that if the function is continous and differentiable then, as it has equal values a and b and if it increases after a, then it will decrease to same value at b after having atleast one local maxima for (a,b) and if it decreases after a, then it will increase to same value at b after having atleast one local minima for (a,b). If the function is constant then the slope will always be zero.

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