ROLLES THEOREM | ROLLES THEOREM in One Short
Channel: IMPETUS GURUKUL
Date: 2022-01-21

#ROLLES_THEOREM
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ROLLES THEOREM | ROLLES THEOREM in One Short

ROLLE'S THEOREM
STATEMENT:-
Let f be a real valued function defined on the closed
interval [a,b] such that
(i) it is continuous on the closed interval [a,b],
(ii) it is differentiable on the open interval (a, b), and,
(iii) f(a)=f(b).
Then, there exists a real number c∈(a,b)such that f^' (c)=0.


GEOMETRICAL INTERPRETATION OF ROLLE'S THEOREM
Let f(x) be a real valued function defined on [a, b] such that the curve y=f(x) is a continuous curve betWeen points A(a,f(a)) and B(b,f(b)) and it is possible to draw a unique tangent at every point on the curve y=f(x) between points A and B. Also, the ordinates at the end points of the interval [a, b] are equal. Then, there exists at least one point (c,f(c)) lying between A and B on the curve y=f(x) where tangent is parallel to x-axis.


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