Question

Lagrange's mean value theorem:​

Answer 1

Answer :

If a function f is defined on the closed interval [a,b] satisfying the following conditions –

i) The function f is continuous on the closed interval [a, b]

ii)The function f is differentiable on the open interval (a, b)

Then there exists a value x = c in such a way that

f'(c) = [f(b) – f(a)]/(b-a)

This theorem is also known as the first mean value theorem or Lagrange’s mean value theorem.

Answer 2

Answer:

The Mean Value Theorem (MVT)

f(b)−f(a)=f′(c)(b−a). This theorem (also known as First Mean Value Theorem) allows to express the increment of a function on an interval through the value of the derivative at an intermediate point of the segment.

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