State Lagrange’s mean value theorem.
Question:

State Lagrange’s mean value theorem.

Solution:

Lagrange’s Mean Value Theorem:

Let $f(x)$ be a function defined on $[a, b]$ such that (i) it is continuous on $[a, b]$ and

(ii) it is differentiable on $(a, b)$.

Then, there exists a real number $c \in(a, b)$ such that $f^{\prime}(c)=\frac{f(b)-f(a)}{b-a}$.