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

 Solution We have
f (x) = tan–1(sin x + cos x), x > 0
Therefore
f ′(x) =
2
1
(cos
sin )
1
(sin
cos )
x
x
x
x
−
+
+
Fig 6