Q. 94.0( 57 Votes )

Prove that the function f given by f (x) = | x – 1|, x R is not differentiable at x = 1.

Answer :

Given: f(x)=|x-1|, x R


because a function f is differentiable at a point x=c in its domain if both its limits as:


are finite and equal.


Now, to check the differentiability of the given function at x=1,


Let we consider the left hand limit of function f at x=1





because, {h < 0 |h|= -h}


= -1


Now, let we consider the right hand limit of function f at x=1





because, {h>0 |h|= h}


= 1


Because, left hand limit is not equal to right hand limit of function f at x=1, so f is not differentiable at x=1.


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