At what point does the function stop decreasing and start increasing?

Rationale

(1, -4)

The function stops decreasing and starts increasing at the point (1, -4), which is the local minimum of the function. This point indicates a transition from a decreasing slope to an increasing slope, reflecting a change in the behavior of the function.

A ((1, -4)) CORRECT

This point is the correct answer because it represents the local minimum where the function changes its direction from decreasing to increasing. At this coordinate, the derivative of the function equals zero, indicating a critical point that signifies the end of a decreasing interval and the beginning of an increasing interval.

B ((3, 0)) YOUR ANSWER

This point does not represent a local minimum or maximum for the function. Instead, it may be part of an increasing segment of the function, where the function is still increasing rather than stopping its decrease. Thus, it does not indicate a point where the function transitions from decreasing to increasing.

C ((-4, 1)) YOUR ANSWER

This point is not relevant in the context of the function's behavior regarding decreasing and increasing intervals. It may be a point on the curve, but it does not indicate a transition point from a decreasing to an increasing function. It could represent a point of increase or a plateau, depending on the function's overall trend.

D ((0, -3)) YOUR ANSWER

At this point, the function is still decreasing before reaching the local minimum at (1, -4). Therefore, it does not mark the transition from decreasing to increasing; rather, it is part of the interval where the function is still falling.

Conclusion

The point (1, -4) is where the function transitions from decreasing to increasing, marking the local minimum. Understanding such critical points is key in calculus for analyzing the behavior of functions, particularly in determining intervals of increase and decrease. The other options do not fulfill this criterion and thus do not represent valid transition points.

At what point does the function stop decreasing and start increasing?

(1, -4)

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test