Published by:
CGP EDU Academic Team
Published on: August 12, 2026
If f(x) = 
and g(x) = 
where 0 < x ≤ 1, then in this interval
Text Solution
Verified by ExpertsThe correct answer is:
C
f ′ (x) = 
, g ′ (x) = 
Let u(x) = sin x – x cos x, so that u ′ (x) = x sin x > 0 for 0 < x ≤ 1. So u(x) > u(0) = 0. So f ′ (x) > 0 for 0 < x ≤ 1. Hence f increasing on (0, 1]. Let v(x) = tan x –x sec 2 x, so that v ′ (x) = –2x sec 2 x tan x < 0 for 0 < x ≤ 1. Thus v(x) < v (0), i.e., g ′ (x) < 0 for 0 < x ≤ 1. So g decreases on (0, 1]
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