If is differentiable at x = 1, find a and b.

LHL =

=

=

= a - b

RHL =

=

=

= 1

Since, f(x) is continuous ,so

LHL = RHL

a - b = 1 - - - - (i)

(LHD at x = 1) =

=

=

=

Using equation (i)

=

=

=

2a

(RHD at x = 1) =

=

=

=

=

= - 1

Since f(x) is differentiable at x = 1,

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

2a = - 1

a =

put a = in equation (i),

a - b = 1

- b = 1

b =

b =

a =