Show that f(x) = is not differentiable at x = 0.

For differentiability,

LHD(at x = 0) = RHD (at x = 0)

(LHD at x = 0) =

=

=

=

=

=

= Not defined

(RHD at x = 3) =

=

=

=

=

= Not defined

Since, LHD and RHD does not exist at x = 0

Hence, f(x) is not differentiable at x = 0