A function f is differentiable in the interval 0

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

If an even function f is differentiable at x=0, then f '(0)=

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

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

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

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

A function f(x) is, continuous in the closed interval [0,1] and differentiable in the open interval [0,1] prove that f'(x_(1))=f(1) -f(0), 0 lt x_(1) lt 1