# Discuss the conti

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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