Find all the critical points of the function?

Question

f(x)=2cosx - |x|
on the interval (-pi,pi)
thank you :)

Answer 1

If 0 sin x= -1/2(No) as in this interval sin x is positive
if -pi<=x<0 f(x) = 2 cos x+x and f¨(x)= -2sinx +1=0
sin x = 1/2 (also impossible)
x=0 is the only critical point as there the derivate does not exist

Answer 2

f(x)=2cosx - |x|
=> f ' (x) = -2 sinx -1

critical points => f ' (x) = 0
=> -2 sinx -1 = 0
=> sinx = -1/2
=> 210 , 330 degs

Answer 3

0, right?
It is not differentiable at that point.
(There are no stationary points in that range)

Answer 4

critical points ?

is not it where dy/dx=0 ?