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What is rolle's theorem?

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What is rolle's theorem?

Posted by Kanishk Gupta 5 years, 3 months ago

CBSE > Class 12 > Mathematics

1 answers

Meghna Thapar 5 years, 3 months ago

Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.

All 3 conditions of Rolle's theorem are necessary for the theorem to be true:

f(x) is continuous on the closed interval [a,b];
f(x) is differentiable on the open interval (a,b);
f(a)=f(b).
The conclusion of Rolle’s theorem is that if the curve is continuous between two points x = a and x = b, a tangent can be drawn at each and every point between x = a and x = b and functional values at x =a and x = b are equal, then there must be atleast one point between the two points x = a and x = b at which the tangent to the curve is parallel to the x-axis.

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