Let `f(x) = max. {|x^2 - 2| x ||,| x |}` then number of points where `f(x)` is non derivable, is :

Let f : R to R be a function defined by f(x) = max. {x, x^(3)} . The set of all points where f(x) is NOT differenctiable is (a) {-1, 1} (b) {-1, 0} (c ) {0, 1} (d) {-1, 0, 1}

Let f:R-> R and g:R-> R be respectively given by f(x) = |x| +1 and g(x) = x^2 + 1 . Define h:R-> R by h(x)={max{f(x), g(x)}, if xleq 0 and min{f(x), g(x)}, if x > 0 .The number of points at which h(x) is not differentiable is

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.

Find number of roots of f(x) where f(x) = 1/(x+1)^3 -3x + sin x

Find the number of points where the function f(x)=max|tanx|,cos|x|) is non-differentiable in the interval (-pi,pi) .

Let f(x)=2x(2-x), 0 le x le 2 . Then find the number of solutions of f(f(f(x)))= (x)/(2) .

Let f(x)=30-2x -x^3 , the number ofthe positive integral values of x which does satisfy f(f(f(x)))) gt f(f(-x)) is

Let f(x+(1)/(x) ) =x^2 +(1)/(x^2) , x ne 0, then f(x) =?