Find the Open Intervals on Which the Function Is Increasing

question 80

Multiple Choice

Find the open intervals on which the function is increasing and decreasing. Identify the function's local and absolute extreme values, if any, saying where they occur.
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• A) increasing on (-3, 0); decreasing on [-5, -3) and (2, 5] absolute maximum at (-5, 1); absolute minimum at (5, -3)
• B) increasing on (-3, 0); decreasing on (-5, -3) and (2, 5) absolute maximum at (-5, 1); local maximum at (0, 0) and (2, 0); Absolute minimum at (5, -3)
• C) increasing on (-3, 0); decreasing on (-5, -3) and (2, 5) absolute maximum at (-5, 1); local minimum at (-3, -3) and (5, -3)
• D) increasing on (-3, 1); decreasing on (-5, -3) and (0, 5) absolute maximum at (-5, 1); no absolute minimum

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Definitions:

Seasonal Variation

A pattern seen in statistical data that occurs at regular intervals due to seasonal factors.

Random Variation

The unpredictability in the behavior or outcome of a process, due to the influence of random factors or noise.

Cyclical Variation

Fluctuations in statistical or economic data that occur periodically over cycles, such as those caused by the business cycle.

Economic Recession

A period of temporary economic decline during which trade and industrial activities are reduced, generally identified by a fall in GDP in two successive quarters.