Short Answer Type
Show that f (x) = tan -1 (sin x + cos x) is a strictly increasing function in the interval 
and strictly decreasing in 
Prove that the function f given by f(x) = log cos x is strictly decreasing on 
and strictly increasing on 
(iv) 
Let f (x) = x100 + sin x – 1 ∴ f ' (x) = 100 x99 + cos x
(i) For – 1 < x < 1, f (x) > 0 is not necessarily true
∴ f (x) is not strictly increasing on (– 1, 1)
(ii) For 0 < x < 1, f ' (x) > 0 ∴ f (x) is strictly increasing on (0, 1).
(iii) 
(iv) 
Find the value of a for which the function f (x) = x3 – 2ax + 6 is increasing for x > 0.
is increasing or decreasing for 
Switch
is an increasing function of x throughout its domain.
