Find the values of a and b, if the function f(x) defined by

is differentiable at x = 1.

Let us find left hand and right-hand derivative of the function f(x).

L.H.D at (x = 1)

(LHD at x = 1) =

=

=

=

= 5

Now let us find Right-hand Derivative of f(x).

(R.H.D at x = 1)

(RHD at x = 1) =

=

=

=

= b

Derivative at (x = 1) =

=

=

=

= 5

Now by definition of differentiability,

L.H.D = R.H.D = Derivative at that point

Therefore, 5 = b = 5

So, a can have any value and b = 5.