A function f(x) is defined as f(x) = x [x] for -1 ≤ x ≤ 3 where [x] defines the greates integer function ≤ x is

(a) continous at all points in the domain of f but non-deriviable at a finite no. of points

(b)Discontinous at all points and hence non deriviable at all points in the domain of f

(c)discontinous at a finite number of points but non deriviable at all points in the domain of f

(d)Discontinous and also non deriviative at a finite number of points of f.

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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