Let f: R → R be a differentiable function such that f((x+y)/3)=(f(x)+f(y))/3 for all x, y ∈ R, and f^′(0)=3. Then the minimum value of the function…

Let $\displaystyle f: \mathbb{R} \rightarrow \mathbb{R}$ be a differentiable function such that $\displaystyle f\left(\frac{x+y}{3}\right)=\frac{f(x)+f(y)}{3}$ for all $\displaystyle x, y \in \mathbb{R}$, and $\displaystyle f^{\prime}(0)=3$. Then the minimum value of the function $\displaystyle g(x)=3+e^x f(x)$, is: