Statement 1: `f(x)=|x-1|+|x-2|+|x-3|` has point of minima at `x=3.` Statement 2: `f(x)` is non-differentiable at `x=3.`

Statement I :The function f(x)=(x^(3)+3x-4)(x^(2)+4x-5) has local extremum at x=1. Statement II :f(x) is continuos and differentiable and f'(1)=0.

Which of the function is non-differential at x=0? f(x)=|"x"^3|

Statement-1 : f(x) = x^(7) + x^(6) - x^(5) + 3 is an onto function. and Statement -2 : f(x) is a continuous function.

If f(x)={'x^2(sgn[x])+{x},0 Option 1. f(x) is differentiable at x = 1 Option 2. f(x) is continuous but non-differentiable at x = 1 Option 3. f(x) is non-differentiable at x = 2 Option 4. f(x) is discontinuous at x = 2

Statement 1: f(x)=(x^3)/3+(a x^2)/2 + x+5 has positive point of maxima for a<-2. Statement 2: x^2+a x+1=0 has both roots positive for a<2.

The number of points where f(x)=|x^(2)-3|x|-4| is non - differentiable is

STATEMENT-1: f(x)=|x-1|+|x+2|+|x-3| has a local minima . and STATEMENT-2 : Any differentiable function f(x) may have a local maxima or minima if f'(x)=0 at some points

Statement -1: f(x) = x^(3)-3x+1 =0 has one root in the interval [-2,2]. Statement-2: f(-2) and f(2) are of opposite sign.

Consider the function f(x)=min{|x^(2)-9|,|x^(2)-1|} , then the number of points where f(x) is non - differentiable is/are

Consider the function f(x)=min{|x^(2)-4|,|x^(2)-1|} , then the number of points where f(x) is non - differentiable is/are