Question

$f(x) = |x| is a function$
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Answer 1

The given function is f(x)=∣x−1∣,x∈R.

It is known that a function f is differentiable at point x=c in its domain if both

limh→0−hf(c+h)−f(c) and limh→0+hf(c+h)−f(c) are finite and equal.

To check the differentiability of the function at x=1,

Consider the left hand limit of f at x=1

limh→0−h∣1+h−1∣−∣1−1∣=limh→0−h∣h∣=limh→0−h−h=−1

Consider the right hand limit of f at x−1

limh→0+h∣1+h−1∣−∣1−1∣=limh→0+hh=1

Since the left and right hand limits of f at x=1 are not equal, f is not differentiable at x=1.

Answer 2

any in-class 9 and from Jnv