Find the critical points of the function: f (x) = x-2sinx-2

The critical points of a function are the points at which the derivative of the function is 0 or does not exist.
In order to find the critical points of a function, you need:
1) Find its derivative;
2) equate it to 0, and solve the equation f ‘(x) = 0;
3) the roots of this equation will be the critical points for our function.
f (x) = x-2sinx-2
1) f ‘(x) = (x-2sinx-2)’ = 1-2 * cosx
2) 1-2cosx = 0
1 = 2cosx
cosx = 1/2
x = Pi / 3 + 2 * Pi * k, where k є Z are critical points.