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.

f(x)=max{(x)/(n),|sin pi x|},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

Let f(x)=max{2sin x,1-cos x},x in(0,pi) then the set of points of non differentiability are(A)phi(B)(pi)/(2)(C){pi-cos^(-1)((3)/(5))}(D){cos^(-1)((3)/(5))}

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

If f(x)={ax^(2)+b,x 1;b!=0, then f(x) is continuous and differentiable at x=1 if

Let f(x)=max{1-x,1+x,2}. Prove that f(x) is continuous at all points but notdifferentiable at x=1 and x=-1

Let f(x)={2x+3 for x 1 if f(x) is everywhere differentiable, prove that f(2)=-4

Let f:(-1,1)rarr R be defined as f(x)=max(-|x|,-sqrt(1-x^(2))), then number of points where it is non-differentiable are equal to (a) 1 (b) 2 (c) 3 (d) 4