Question

Define Mean Value Theorem​

Answer 1

Answer:

In mathematical analysis, the intermediate value theorem states that if f is a continuous function whose domain contains the interval [a, b], then it takes on any given value between f(a) and f(b) at some point within the interval.

Step-by-step explanation:

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Answer 2

Suppose f(x) is a function that satisfies below conditions:

f(x) is Continuous in [a,b]

f(x) is Differentiable in (a,b)

Then, there exists a number c, s.t. a < c < b and

f(b) – f(a) = f ‘(c) (b – a)

Special Case:

When f(a) = f(b). Then, there exists at least one c with a < c < b such that f'(c) = 0. This case is known as Rolle’s Theorem.