Chapter 4: Applications of Derivatives - Section 4.2 - The Mean Value Theorem - Exercises 4.2 - Page 198: 28

Yes, see explanations.

Step 1. Assume $g(x)=2x+5$, we have $g'(x)=2$. Step 2. Based on the Corollary 2, because $f'(x)=g'(x)$, we have $f(x)=g(x)+C$ where $C$ is a constant. Step 3. Using the condition that $f(0)=5$, we have $f(0)=g(0)+C$ and $5=5+C$, thus $C=0$ Step 4. We conclude that $f(x)=2x+5$ for all $x$.