Question

How do you find the mean value theorem applies $?$

Answer 1

Applicability of mean value theorem:

Mean value theorem is one of the most useful tools in both differential and integral calculus.

It has very important consequences in differential calculus and helps us to understand the identical behaviour of different functions.

Mean value theorem is also known as Lagrange’s mean value theorem. This theorem is abbreviated as MVT.

Suppose $f\left(x\right)$ is a function that satisfies below conditions:

1. $f\left(x\right)$ is continuous in $[a,b]$
2. $f\left(x\right)$ is differentiable in $(a,b)$

Then, there exists a number$c,$ such that $a<c<b$ and $f\left(b\right)–f\left(a\right)=f‘\left(c\right)(b–a)$

Mean value theorem (abbreviated to MVT) applied to a function, if the function is continuous in$[a,b]$ and differentiable in $(a,b).$

Hence, in this way we can find where the mean value theorem is applicable.