Question

f(x)=tan x-x state the function?

Answer 1

Answer

Correct option is

A

Always increases

f(x)=tanx−x

f

′

(x)=sec(x)

2

−1>0

Or

sec(x)

2

>1

Now

cos(x)ϵ[−1,1]

Hence

sec(x)ϵ(−∞,−1]∪[1,∞).

Thus

sec

2

(x)ϵ[1,∞)

Hence

f

′

(x)>0 for all x.

Hence

f(x) is always increasing.