Point OF Non Differentiabilty, Max & Min OF g(x) , Diff OF Modulus function, Differentiabilty in [a,b]

Reasons OF Non Differentiability || Modulus based questions to check continuity & differentiabilty || Theorem on differentiabilty

Let f(x)=max{|x^(2)-2|x||,|x|} and g(x)=min{|x^(2)-2|x||,|x|} then prove that f(x) in not differentiable at 5 points and g(x) is not differentiable at 7 points.Also draw the graph of both f(x) and g(x) .

Importance of critical point in drawing the graph of modulus function

If the number of points of non differentiable of f(x)=max{sin x ,cos x, 0} in (0, 2n pi) is Pn then find the value P

Given that g(x) is a non constant linear function defined on R-

Let there are two functions defined of f(x)="min"{|x|,|x-1|} on the basis of above information answer the following question: Points of non-differentiability of f(x) in (-1,1)

If f(x) and g(x) are non- periodic functions, then h(x)=f(g(x))is