Show that the function

F(x) =

Is continuous but not differentiable at x = 1.

F(x) =

For continuity at x = 1

F(1) = - (2(1) - 3) = 1

LHL =

=

=

= sin

= 1

RHL =

=

=

= - 1( - 1)

= 1

LHL = RHL = f(1)

So, f(x) is continuous at x = 1

For differentiability at x = 1

(LHD at x = 1) =

=

=

=

=

= 0

(RHD at x = 1) =

=

=

=

=

= - 2

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

Hence, f(x) is continuous but not differentiable at x = 1.