In this case, we have x – 1 > 0,
x + 2 > 0 and  x – 3 > 0 So f ′(x) > 0 when x > 3 Thus,  f  is increasing in the interval (3, ∞) Example 34 Show that the function f given by
f (x) = tan–1(sin x + cos x), x > 0
is always an increasing function in 0 4
, π

