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) (c)
Clearly by (a) and (b) above, f is neither increasing nor decreasing in (0, 2π) Example 10 Find the intervals in which the function f given by f(x) = x2 – 4x + 6 is
(a) increasing
(b)  decreasing
Solution We have
f (x)
= x2 – 4x + 6
or
f ′(x) = 2x – 4
Therefore, f ′(x) = 0 gives x = 2