Let g(x)=3 f(x/3)+f(3-x) and f^′ ′(x)>0 for all x ∈(0,3). If g is decreasing in (0, α) and increasing in ( α, 3 ), then 8 α is:

Let $\displaystyle g(x)=3 f\left(\frac{x}{3}\right)+f(3-x)$ and $\displaystyle f^{\prime \prime}(x)>0$ for all $\displaystyle x \in(0,3)$. If $\displaystyle g$ is decreasing in $\displaystyle (0, \alpha)$ and increasing in ( $\displaystyle \alpha, 3$ ), then $\displaystyle 8 \alpha$ is :