Question
Prove that the function f (x) = cos x is
(i) strictly increasing in 
(ii) strictly decreasing in 
(iii) neither increasing nor decreasing in 
Solution
Here f (a) = cos x ⇒ f ' (x) = – sin x
(a) In 
, f '(x) = – sin x > 0
∴ f (x) is strictly increasing in (– 
, 0)
(b) In 
f ' (x) = – sin x < 0
∴ f (x) is strictly decreasing in (0, 
)
(c) Now f (x) is strictly increasing in (– 
, 0) and strictly decreasing in 
∴ f (x) is neither increasing nor decreasing in 
.
