Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If f ″ (x) > 0 ∀ x ∈ R, f ′ (4) = 0 and
g(x) = f (cot 2 x – 2cot x + 5) ; 0 < x < 
, then
A
g(x) is increasing in 
B
g(x) is decreasing in 
C
g(x) is increasing in 
D
g(x) is decreasing in 
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(c, d)
f ″ (x) > 0 ⇒ f ′ (x) is increasingg ′ (x) = f ′ (cot
2 x – 2 cot x + 5)
(– 2 cot x. cosec 2 x + 2 cosec 2 x)
= f ′ ((cot x–1) 2 + 4) 2 cosec 2 x (1 – cot x)
g ′ (x) < 0 ∀ x ∈ 
⇒ g(x) is decreasing in 
g ′ (x) > 0 ∀ x ∈ 
⇒ g(x) is increasing in 
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