JEE Main 2024 Mathematics question
Let and f″(x) > 0 for all x ∈ (0, 3). If g is decreasing in (0, α) and increasing in (α, 3), then 8α is :
Answer: (B)
Solution
g′(x) = f′(x/3) − f′(3 − x). Since f″ > 0, f′ is increasing, so g′(x) < 0 iff x/3 < 3 − x, i.e. x < 9/4. So α = 9/4 and 8α = 18.