99 Percentile Qs Bank for JEE MainMathematicsApplication of Derivatives
Let R * = R - ( 2 k - 1 ) π 2 / k ∈ I . The function f   :   R * → R is defined as f x = tan x - x , then f x is
Options
- Aan increasing function
- Ba decreasing function
- Cminimum at x = 0
- Dperiodic function
Correct answer
A. an increasing function
Step-by-step solution
Given: f x = tan x - x Differentiating on both sides, we get f ' x = sec 2 x - 1 As,   sec x ∈ ( - ∞ , - 1 ] ∪ [ 1 , ∞ ) ∴ sec 2 x ∈ [ 1 , ∞ ) ∴ sec 2 x - 1 ≥ 0 ∴ f ' x ≥ 0   for all   x ∈ R * ∴ f x is an increasing function. Hence, option 1 is correct.