If `f(x) = {{:({x+(1)/(3)}[sin pi x]",",0 le x lt 1),([2x]sgn(x - (4)/(3))",",1 le x le 2):}`, where [.] and {.} denotes greatest integerd and fractional part of x respectively, then the number of points, which is not differentiable, is

If f(x) = {{:(|1-4x^(2)|",",0 le x lt 1),([x^(2)-2x]",",1 le x lt 2):} , where [] denotes the greatest integer function, then

If f(x) = {{:(|1-4x^(2)|",",0 le x lt 1),([x^(2)-2x]",",1 le x lt 2):} , where [] denotes the greatest integer function, then

Consider a function defined in [-2,2] f (x)={{:({x}, -2 le x lt -1),( |sgn x|, -1 le x le 1),( {-x}, 1 lt x le 2):}, where {.} denotes the fractional part function. The number of points for x in [-2,2] where f (x) is non-differentiable is:

If f(x)={{:(,x[x], 0 le x lt 2),(,(x-1)[x], 2 le x lt 3):} where [.] denotes the greatest integer function, then

f(x) {(|x-(1)/(2)|",",0 le x lt 1),(x[x]",",1 le x lt 2):} where [.] denotes the greatest integer function. Show that f(x) is continuous at x=1 but not differentiable at x=1.

Let f (x)= {{:(x [x] , 0 le x lt 2),( (x-1), 2 le x le 3):} where [x]= greatest integer less than or equal to x, then: The number of values of x for x in [0,3] where f (x) is non-differentiable is :

Let f (x)= {{:(x [x] , 0 le x lt 2),( (x-1), 2 le x le 3):} where [x]= greatest integer less than or equal to x, then: The number of values of x for x in [0,3] where f (x) is non-differentiable is :

If f(x)={{:(,x[x], 0 le x lt 2),(,(x-1)[x], 2 le x lt 3):} where [.] denotes the greatest integer function, then continutity and diffrentiability of f(x)

If f(x)={{:(,x[x], 0 le x lt 2),(,(x-1)[x], 2 le x lt 3):} where [.] denotes the greatest integer function, then continutity and diffrentiability of f(x)

If f(x)={{:(,x[x], 0 le x lt 2),(,(x-1)[x], 2 le x lt 3):} where [.] denotes the greatest integer function, then (x) is continuous at x=2