Answer :

f(x) =

f(x) =

We know that a polynomial and a constant function is continuous and differentiable every where. So, f(x) is continuous and differentiable for x ( - 1,0) and x (0,1) and (1,2).

We need to check continuity and differentiability at x = 0 and x = 1.

Continuity at x = 0

= 1

= 1

F(0) = 1

Since, f(x) is continuous at x = 0

Continuity at x = 1

= 1

= 1

F(1) = 1

= 1

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

**For differentiability,**

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

Differentiability at x = 0

(LHD at x = 0) =

=

=

= 2

(RHD at x = 0) =

=

=

= 0

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

So, f(x) is differentiable at x = 0.

**For differentiability,**

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

Differentiability at x = 1

(LHD at x = 1) =

=

= 0

(RHD at x = 1) =

=

=

Since, f(x) is not differentiable at x = 1.

So, f(x) is continuous on ( - 1,2) but not differentiable at x = 0, 1

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