Question

please explain..... difference between Mean value theorem and Roll's theorem........ copied answer will be reported...​

Answer 1

Rolle's theorem, in analysis, special case of the mean-value theorem of differential calculus. 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.

The difference really is that the proofs are simplest if we prove Rolle's Theorem first, then use it to prove the Mean Value Theorem.

Answer 2

it's not copied

Step-by-step explanation:

(The Mean Value Theorem claims the existence of a point at which the tangent is parallel to the secant joining (a, f(a)) and (b, f(b)). Rolle's theorem is clearly a particular case of the MVT in which f satisfies an additional condition, f(a) = f(b).)

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