F' (x) >0 если f (x) = cosx - x/2

Решение

F' (x) >0 если f (x) = cosx - x/2

F' (x) = - sunx - 1/2

- sunx - 1/2 > 0

- sinx > 1/2

sinx < - 1/2

- π - arcsin (-1/2) + 2πn < x < arcsin (-1/2) + 2πn, n ∈ Z

- π - ( - π/6) + 2πn < x < - π/6 + 2πn, n ∈ Z

- 5π/6 + 2πn < x < - π/6 + 2πn, n ∈ Z