1. **State the problem:** Determine which option (A, B, C, or D) correctly represents the function $f$ defined over $[-5,6]$ with the given derivative and initial condition. 2. **Recall the function from previous work:** $$ f(x) = \begin{cases} x + 6 & -5 \leq x \leq -3 \\ 3 & -3 < x \leq -1 \\ 2 - x & -1 < x \leq 2 \\ 0 & 2 < x \leq 6 \end{cases} $$ 3. **Check each option (A, B, C, D) against this piecewise function:** - Verify the values at key points $x = -5, -3, -1, 2, 6$. - Verify slopes on each interval match the derivative step function. 4. **Conclusion:** The correct answer is the option that matches the above piecewise function exactly. Since the problem does not provide the explicit options A, B, C, or D, please compare the given options to the function above to select the correct one.