The problem asks us to determine the intervals where a polynomial function is decreasing based on its behavior. Let’s break down the information provided:

1. The function goes up from the left, passing through the point (-1, 0).

   • This means that the function is increasing as it approaches $x = -1$.

2. It reaches a relative maximum at $(0, 5)$.

   • This indicates that the function starts decreasing after $x = 0$.

3. It then goes down to a relative minimum at $(1, 4)$.

   • The function is decreasing between $x = 0$ and $x = 1$.

4. Finally, it goes back up as it moves to the right (for $x > 1$).

   • The function starts increasing again for $x > 1$.

Analyzing the Decreasing Intervals

• The function decreases between the maximum point at $x = 0$ and the minimum point at $x = 1$.

Thus, the correct interval where the function is decreasing is $(0, 1)$.

Conclusion

The correct answer is:

d) $(0, 1)$

---

Would you like more details or have any questions? Here are 5 related questions that could further your understanding:

1. What is the formal definition of an increasing and decreasing function?
2. How do you determine intervals of increase and decrease for polynomial functions using derivatives?
3. What are critical points, and how do they relate to relative maxima and minima?
4. How can you sketch a polynomial function given its relative extrema?
5. What is the significance of inflection points in understanding the concavity of a function?

Tip: To determine where a function is increasing or decreasing, find the derivative and analyze its sign across different intervals.