Chapter 4 - Applications of the Derivative - 4.3 The Mean Value Theorem and Monotonicity - Exercises - Page 190: 60

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

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*}