Explain whether f(x) is continuous and has a derivative at the point x=1 were `f(x)=x` for `0<=x<=1` `=2-x if x>1`

Examine whether f (x) = |x| has a derivative at x = 0 .

Examine whether f(x) = |x| has a derivative at x = 0.

Examine whether f(x)=|x+1| has a derivative at x = - 1 .

Examine whether f (x)=|2x| has a derivative at x = 0

Examine whether the function f(x)=x^2 is continuous at x=0

Let f'(x)=3x^2sin1/x-xcos1/x , if x!=0\ ; f(0)=0 and f(1//pi)=0 then: f(x) is continuous at x=0 f(x) is non derivable at x=0 f'(x) is continuous at x=0 f'(x) is non derivable at x=0

If f(x) is continuous and differentiable on R and its derivative vanishes for 2 values of x only. Then f(x) cannot vanish for more than ........ points.

Let f(x) = x+ |x|. Show that f is continuous but not derivable at x = 0

Let f (x) = |x-2| and g (x) = f (f (x)). Then derivative of g at the point x =5 is

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