1. **Problem:** Find the first derivative $f'(x)$ and second derivative $f''(x)$ of the function $f(x) = 3x + 2$. 2. **Formula and rules:** - The derivative of $ax + b$ is $a$. - The second derivative of a linear function is always 0 because the first derivative is a constant. 3. **First derivative:** $$f'(x) = \frac{d}{dx}(3x + 2) = 3$$ 4. **Second derivative:** $$f''(x) = \frac{d}{dx}(3) = 0$$ 5. **Explanation:** - Since $f(x)$ is linear with slope 3, its derivative is constant 3. - The second derivative is zero because the slope does not change. 6. **Graph description:** - $f(x) = 3x + 2$ is a straight line with slope 3. - $f'(x) = 3$ is a horizontal line at $y=3$. - $f''(x) = 0$ is the $x$-axis. Final answer: $$f'(x) = 3, \quad f''(x) = 0$$