Question

f'(x)>0 если f(x)= cosx - x/2

Answer 1

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