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.

f(x) = |x| on [ – 1, 1]

For differentiability at x=0,

{Since f(x)= – x, x<0}

= – 1

{Since f(x)= x, x>0}

= 1

⇒ f(x) is not differential at x=0

∴ Lagrange’s mean value theorem is not applicable for the function f(x) = |x| on [ – 1, 1].