Published by:
CGP EDU Academic Team
Published on: August 12, 2026
The function f(x) = 2 log (x –2) –x 2 + 4x + 1 increases in the interval:
Text Solution
Verified by ExpertsThe correct answer is:
B
(b and c)
f ′ (x) = 
–2x + 4 = 
–2 (x –2)
= 2 
Therefore, f ′ (x) > 0 only if (i) 1 – (x –2) 2 > 0 and x –2 > 0, or (ii) 1 – (x –2) 2 < 0 and x –2 < 0. In the first case, we have (x –3) (x –1) < 0 and
x > 2. That is, 1 < x < 3 and x > 2, so that x ∈ (2, 3). The second case is not possible as the domain of f(x) is {x : x > 2}. Hence f(x) increases on (2, 3) and, since (5/2, 3) ⊂ (2, 3), it increase on (5/2, 3) as well.
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