Question 15

The function stops decreasing and starts increasing at the point (1, -4).

The function transitions from decreasing to increasing at the point (1, -4), indicating a local minimum where the slope changes from negative to positive.

A) (1, -4)

This option is correct because it represents the point where the function ceases to decrease. At this coordinate, the derivative of the function equals zero, indicating a change in direction from decreasing to increasing.

B) (3, 0)

This option is incorrect as (3, 0) does not represent a point of inflection or a local minimum. Instead, it is a point where the function may still be increasing, but it does not mark the transition from decreasing to increasing.

C) (-4, 1)

This option is also incorrect because (-4, 1) does not indicate a local minimum or any point where the function transitions from decreasing to increasing. It does not provide information about the slope or behavior of the function around this point.

D) (0, -3)

This option is incorrect as well. The point (0, -3) does not signify a change in the direction of the function. It is simply a point on the graph and does not indicate where the function stops decreasing.

Conclusion

The correct answer, (1, -4), is definitively the point where the function changes from decreasing to increasing, as indicated by the behavior of the function at that coordinate. All other options fail to represent such a transition, demonstrating that they do not mark the critical point of interest in the function's behavior.