Published by:
CGP EDU Academic Team
Published on: August 12, 2026
On which of the following intervals is the function x 100 + sin x – 1 decreasing ?
Text Solution
Verified by ExpertsThe correct answer is:
D
ƒ(x) = x 100 + sin x – 1 ⇒ ƒ ′ (x) = 100 x 99 + cos x.
If 0 < x < π /2, then ƒ ′ (x) > 0, therefore ƒ(x) is increasing on (0, π /2).
If 0 < x < 1, then 100 x 99 + cos x > 0
[ x lies between 0 and 1 radian]
⇒ ƒ ′ (x) = 100 x 99 + cos x > 0
⇒ ƒ (x) is increasing on (0, 1).
If π /2 < x < π , then 100 x 99 > 100
[ x > 1, ∴ x 99 > 1]
⇒ 100 x 99 + cos x > 0
[ cos x ≥ –1, ∴ 100 x 99 + cos x > 99]
⇒ ƒ ′ (x) > 0 ⇒ f(x) is increasing on ( π /2, π ).
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