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CGP EDU Academic Team
Published on: August 13, 2026
If g(x) = f(x) + f(1 – x ) and f ′′ (x) < 0, 0 ≤ ≤ x ≤ 1, then
Text Solution
Verified by ExpertsThe correct answer is:
A
f ′′ (x) < 0 ⇒ f ′ (x) is decreasing
g is increasing ⇒ g ′ (x) > 0
⇒ f ′ (x) – f ′ (1 – x) > 0 ⇒ f ′ (x) > f ′ (1 – x)
⇒ x < 1 – x ⇒ x < 
∴ g is increasing in x ∈ (0, 1/2)
g is decreasing when g ′ (x) < 0
f ′ (x) < f ′ (1 – x)
x > 1 – x ⇒ x > 1/2
∴ g is decreasing x ∈ (1/2, 1)
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