refer to the given graph. list all intervals in which the graph is increasing and all the intervals in which the graph is decreasing. if there are more than one intervals, separate them by a comma. use open intervals and exact values. no space between commas.

all intervals on which the graph is increasing:
all intervals on which the graph is decreasing:

Question

refer to the given graph. list all intervals in which the graph is increasing and all the intervals in which the graph is decreasing. if there are more than one intervals, separate them by a comma. use open intervals and exact values. no space between commas.

all intervals on which the graph is increasing:
all intervals on which the graph is decreasing:

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Critical Points", "Local Extrema" ], "new_concepts": [ "Increasing and Decreasing Intervals", "Interval Notation" ], "current_concepts": [ "Critical Points", "Local Extrema", "Increasing and Decreasing Intervals", "Interval Notation" ] } ## Identify local extrema Using the **Critical Points** and **Local Extrema** knowledge points $$ \begin{aligned} &\text{Local maximum at } x = -2\ &\text{Local minimum at } x = 2 \end{aligned} $$ ## Determine increasing intervals Using the **Local Extrema** knowledge point $$ \begin{aligned} &\text{Graph rises on } (-\infty, -2) \text{ and } (2, \infty)\ &\text{Increasing intervals: } (-\infty,-2),(2,\infty) \end{aligned} $$ ## Determine decreasing intervals Using the **Local Extrema** knowledge point $$ \begin{aligned} &\text{Graph falls on } (-2, 2)\ &\text{Decreasing interval: } (-2,2) \end{aligned} $$ Refer to the given graph. List all intervals in which the graph is increasing and all the intervals in which the graph is decreasing. If there are more than one intervals, separate them by a comma. Use open intervals and exact values. No space between commas. All intervals on which the graph is increasing: $(-\infty,-2),(2,\infty)$ All intervals on which the graph is decreasing: $(-2,2)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Calculus", "Increasing and Decreasing Intervals" ] }

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Question

Explanation:

Identify local extrema

Determine increasing intervals

Determine decreasing intervals

Answer: