Pregunta
Describe how the values of
As the values of
the
[Select]
As the value of
[Select ]
As the values of
the
[Select]
As the value of
[Select ]
Ask by Jimenez Murray. in the United States
Jan 23,2025
Solución de inteligencia artificial de Upstudy
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A maximum occurs when y changes from increasing to decreasing, and a minimum occurs when y changes from decreasing to increasing.
Solución
When analyzing the behavior of a function to determine where it reaches maximum or minimum values, it’s essential to observe how the
-
Maximum Value:
- Behavior: A maximum value occurs at a point where the function changes its trend from increasing to decreasing.
- Explanation: As
increases, the -values of the function are getting larger (increasing). When the function reaches a peak, the -values stop increasing and begin to decrease. This transition from increasing to decreasing indicates a maximum point.
Completion:- The
-values change from increasing to decreasing.
-
Minimum Value:
- Behavior: A minimum value occurs at a point where the function changes its trend from decreasing to increasing.
- Explanation: As
increases, the -values of the function are getting smaller (decreasing). When the function reaches the lowest point, the -values stop decreasing and begin to increase. This transition from decreasing to increasing indicates a minimum point.
Completion:- The
-values change from decreasing to increasing.
Summary:
- Maximum:
-values change from increasing to decreasing. - Minimum:
-values change from decreasing to increasing.
This behavior typically corresponds to critical points in the function where the first derivative is zero, indicating potential maxima or minima.
Visual Representation:
In the graph above, the peak represents a maximum where the function transitions from increasing to decreasing, and the trough represents a minimum where it transitions from decreasing to increasing.
Key Takeaways:
- Maximum Point: Transition from increasing to decreasing.
- Minimum Point: Transition from decreasing to increasing.
Answer Summary:
• A maximum occurs where y changes from increasing to decreasing.
• A minimum occurs where y changes from decreasing to increasing.
• A minimum occurs where y changes from decreasing to increasing.
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When examining how the values of
On the flip side, a minimum value pops up when the
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