Find the global extrema of the function

Question

find the global extrema of the function f (x) = cos(2x) − x for x ∈ [− π/2 , π/2 ].

Answer 1

f'(x) = - 2sin(2x) - 1 = 0; sin(2x) = - 1/2; 2x = - π/6; x = - π/12; or 2x = - 5π /6, x = - 5π/12

f(- π/2) = - 1 + π/2; f(- 5π/12) = - √3/2 + 5π/12; f(- π/12) = √3/2 + π/12 (abs max), f(π/2) = - 1 - π (abs min)