Find whether the following function is differentiable at x = 1and x= 2 or not:

f(x) =

Differentiability at x = 1

For differentiability,

LHD(at x = 1) = RHD (at x = 1)

(LHD at x = 1) =

=

= 1

(RHD at x = 1) =

=

=

= - 1

Since, (LHD at x = 1)(RHD at x = 1)

So, f(x) is not differentiable at x = 1

Differentiable at x = 2

(LHD at x = 2) =

=

=

= - 1

(RHD at x = 2) =

=

=

= - 1

Since, (LHD at x = 2) = (RHD at x = 2)

So, f(x) is differentiable at x = 2.