#### Answer

$$f(x) \leq 3x+2$$

#### Work Step by Step

By using the MVT on $[0,4]$, we get
\begin{align*}
\frac{f(4)-f(0)}{4-0}&=f^{\prime}(x)\\
\frac{f(4)-2}{4} &\leq 3\\
f(4)& \leq 14
\end{align*}
Applying the MVT on $[0,x]$, we get:
\begin{align*}
\frac{f(x)-f(0)}{x-0}&=f^{\prime}(x)\\
\frac{f(x)-2}{x} &\leq 3\\
f(x)& \leq 3x+2
\end{align*}