Let g(x) = 3f(x/3) + f(3 - x) where f''(x) > 0 for all x ∈ (0,3).… | JEE Main 2024 Mathematics PYQ

MCQMediumJEE Main 2024 · 27 January, Shift 2Derivatives of Functions

Let $g(x) = 3f\left(\frac{x}{3}\right) + f(3 - x)$ where $f''(x) > 0$ for all $x \in (0,3)$ . If $g$ is decreasing in $(0, \alpha)$ and increasing in $(\alpha,3)$ , what is $8\alpha$ ?

A
$24$
B
$0$
C
$18$
D
$20$

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