f(x)= -1.x  for -1<=x<0

f(x)= 0 for  0<=x<1

f(x)=x  for 1<=x<2

f(x)=2x  for 2<=x<3

f(x)=3x for x=3

therefore f(x) is continuous but since it has peaks at 1,0,1,2,3 it is not differentiable at these points  so (a) is the answer

Dear Tushar Watts,

f(x)= -1.x for -1<=x<0

f(x)= 0 for 0<=x<1

f(x)=x for 1<=x<2

f(x)=2x for 2<=x<3

 f(x)=3x for x=3

 we also observe that f(1+) is not equal to f(1-),f(2+) is not equal to f(2-),f(3) is not equal to f(3-). Hence it is not continuous at finite number of points. And it is also not differentiable at points 0,1,2,3. It is not continuous at 1,2,3, so its not differentiable at these points, and there is a sharp edge at 0, so it is also not differentiable at 0. Hence it is also not differentiable at finite number of points. So answer is (d).

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