Question 22
The function f (x) = tan x β x
always increases
(B) always decreases
(C) never increases
(D) sometimes increases and sometimes decreases.
Given π(π₯) = tan π₯ β π₯
Finding π^β² (π)
π^β² (π₯)=γπππγ^π π βπ
Now, we need to check if π(π) is increasing or decreasing
Checking sign of π^β² (π)
π^β² (π₯)=γπππγ^π π βπ
Now,
π¬ππ π π (ββ,βπ]βͺ[π,β)
So,
γπππγ^π π π [1,β)
Therefore, we can write this as
πβ€γπππγ^π πβ€β
1βπβ€γπ ππγ^2 π₯βπβ€ββπ
0β€γπππγ^π πβπβ€β
Thus,
γπ ππγ^2 π₯β1β₯0
β΄ π^β² (π)>π for all values of x
Hence, π(π) always increases.
So, the correct answer is (A)

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.