# Discuss the Application and conclusion of Lagranges’s Mean Value Theorem on the function f (x) = |x| oninterval [-1, 1].

Grade:11

## 2 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
9 years ago

if a functionfiscontinuouson theclosed interval[a,b], wherea<b, and differentiable on theopen interval(a,b), then there exists a pointcin (a,b) such that

$f'(c) = \frac{f(b) - f(a)}{b-a} \, .$
f(-1)=1 and f(1)=1, but the function is not differentiable at x=0, f'(0-)=-1 and f'(0+)=1, and we cant apply mean value theorem on this function.
Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
9 years ago
f(1)=f(-1)=0 f(0-)=d(-x)/dx=-1 f(0+)=d(x)/dx=1 the function is not differential between -1 and 1 hence, the mean value theorem can`t be applied. Sher Mohammad B.Tech, IIT Delhi