Show that f(x) = |x - 3| is continuous but not differentiable at x = 3.

f(x) = |x – 3|

Therefore we can write it as,

f(3) = 3 - 3 = 0

LHL =

=

=

=

RHL =

=

=

= 0

LHL = RHL = f(3)

Since, f(x) is continuous at x = 3

(LHD at x = 3) =

=

=

=

= - 1

(RHD at x = 3) =

=

=

=

= 1

(LHD at x = 3)(RHD at x = 3)

Hence, f(x) is continuous but not differentiable at x = 3.