Lagrange’s mean value theorem states that if a function f(x) is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there is at least one point x=c on this interval, such that

f(b)−f(a)=f′(c)(b−a)

This theorem is also known as First Mean Value Theorem.

Here,

⇒ f(x) exists for all values of x except 0

⇒ f(x) is discontinuous at x=0

∴ f(x) is not continuous in [ – 1, 1]

Hence the lagrange’s mean value theorem is not applicable to the