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Can some one explain that what is Rolle' s Theorem ??????????????????
Dear Rahul,
Let f be continuous on a closed interval [a, b] and differentiable on the open interval (a, b). If f(a) = f(b), then there is at least one point c in (a, b) where f '(c) = 0.
It just says that between any two points where the graph of the differentiable function f (x) cuts the x-axis there must be a point where f'(x) = 0.
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Askiitians Experts
MOHIT
the statement/definition of ROLLEs Theorem is as follows:-
If y=f(x) is
(i)continuous function in[a,b]
(ii)Derivable function in (a,b)
(iii)f(a)=f(b)
Then, THERE EXISTS at least one Real number ''c''; cε(a,b) such that f''(c)=o
we have to observe that,
NOTE:1 The converse of the Rolle''s theorem,need not be true.
that means, If f''(c)=o,then
(i)f(x) need not be continuous on [a,b]
(ii)f(x) need not be derivable on (a,b)
(iii)f(a)=f(b) need not be true
NOTE:2 The geometrical interpretation of ROLLEs is there exists a tangent at x=c which is parallel to x-axis.
Here is the Rolle''s theorem,
Thanking you
Suchandar
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