If `f(x)=max{x^2+2a x+1, b}` has two points of non-differentiability, then prove that `a^2>1-b`

If the function f(x)=| x^2 + a | x | + b | has exactly three points of non-derivability, then

Draw the graph of the function f(x)= x- |x-x^(2)|, -1 le x le 1 and find the points of non-differentiability.

If f(x) = |1 -x|, then the points where sin^-1 (f |x|) is non-differentiable are

f(x) = max{x/n, |sinpix|}, n in N . has maximum points of non-differentiability for x in (0, 4) , Then n cannot be (A) 4 (B) 2 (C) 5 (D) 6

Find x where f(x)=max {sqrt(x(2-x)),2-x} is non-differentiable.

Find x where f(x) = max {sqrt(x(2-x)),2-x} is non-differentiable.

If f(x) = |x+1|(|x|+|x-1|) , then at what point(s) is the function not differentiable over the interval [-2, 2] ?

Find the number of points of non-diferentiability for f(x)=max{||x|-1|,1//2} .

The function f(x)=x^(1/3)(x-1) has two inflection points has one point of extremum is non-differentiable has range [-3x2^(-8/3),oo)

The function f(x)=x^(1/3)(x-1) has two inflection points has one point of extremum is non-differentiable has range [-3x2^(-8/3),oo)