Question

prove Rolle’s mean value theorem​

Answer 1

Step-by-step explanation:

Instead, we shall use the Lemma to prove the Mean Value theorem. Rolle's theorem Let f(x) be a function which is continuous on the closed interval [a, b] and differentiable on every point of the interior of [a, b]. Suppose that f(a) = f(b). Then there is a point c ∈ [a, b] where f (c) = 0.

Answer 2

Rollé theorems has three steps for verification:

Verify Rolle's theorem for the function f(x)= x2-5x+4 on [1, 4].

• Rolle′s theorem states that if a function f(x) is continuous in [a,b]and differentiable in interval (a,b),
• then, if f(a)=f(b), then f′(c)=0, where c lies in (a,b).

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