Example 9 Prove that the function given by f (x) = cos x is
(a)
decreasing in (0, π)
(b)
increasing in (π, 2π), and
(c)
neither increasing nor decreasing in (0, 2π) Rationalised 2023-24
APPLICATION OF DERIVATIVES
155
Fig 6 4
Solution Note that f ′(x) = – sin x
(a)
Since for each x ∈ (0, π), sin x > 0, we have f ′(x) < 0 and so f is decreasing in
(0, π) (b)
Since for each x ∈ (π, 2π), sin x < 0, we have f ′(x) > 0 and so f is increasing in
(π, 2π)