Question -
Answer -
Given f(x) = cos x
⇒ 
⇒ f’(x)= –sin x
Taking different region from 0 to 2π
Let x ∈ (0,π).
⇒ Sin(x)> 0
⇒ –sinx < 0
⇒ f’(x)< 0
Thus f(x) is decreasing in (0, π)
Let x ∈ (–π,o).
⇒ Sin(x) < 0
⇒ –sinx > 0
⇒ f’(x)> 0
Thus f(x) is increasing in (–π, 0).
Therefore, from above condition we find that
⇒ f(x) is decreasing in (0, π) and increasing in (–π, 0).
Hence, condition for f(x) neither increasing nor decreasing in(–π, π)