Published by:
CGP EDU Academic Team
Published on: August 12, 2026
If ƒ(x) = 
and g(x) = 
, where 0 < x ≤ 1,
then in this interval -
Text Solution
Verified by ExpertsThe correct answer is:
C
Let ƒ(x) = 
⇒ ƒ ′ (x) = 
Let u(x) = sin x – x cos x so u ′ (x) = cos x – cos x + x sin x = x sin x > 0 for 0 < x ≤ 1. Hence u is an increasing so u(x) > u(0) = 0. Thus ƒ ′ (x) > 0 for 0 < x ≤ 1. i.e. ƒ is an increasing function. Now
g ′ (x) = 
. Let v(x) = tan x – x sec 2 x.
Since v ′ (x) = sec 2 x
– sec 2 x – 2x sec 2 x tan x = – 2x sec 2 x tan x < 0 for 0 < x ≤ 1. Hence v(x) < v(0) = 0 so g ′ (x)< 0 for 0 < x ≤ 1. Thus g is a decreasing function.
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