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 (-2, 0) and (2, 4); decreasing on (0, 2); absolute maximum at (4, 6); absolute minimum at (-2, 0) and (2, 0)
B) increasing on (2, 4); decreasing on (0, 2); absolute maximum at (4, 6); local maximum at (0, 2); absolute minimum at (-2, 0) and (2, 0)
C) increasing on (-2, 0) and (2, 4); decreasing on (0, 2); absolute maximum at (4, 6); local maximum at (0, 2); absolute minimum at (-2, 0) and (2, 0)
D) increasing on (-2, 0) and (2, 4); decreasing on (0, 2); absolute maximum at (4, 6) and(0,2); absolute minimum at (-2, 0) and (2, 0)

Question

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 (-2, 0) and (2, 4); decreasing on (0, 2); absolute maximum at (4, 6); absolute minimum at (-2, 0) and (2, 0) 
B) increasing on (2, 4); decreasing on (0, 2); absolute maximum at (4, 6); local maximum at (0, 2); absolute minimum at (-2, 0) and (2, 0) 
C) increasing on (-2, 0) and (2, 4); decreasing on (0, 2); absolute maximum at (4, 6); local maximum at (0, 2); absolute minimum at (-2, 0) and (2, 0) 
D) increasing on (-2, 0) and (2, 4); decreasing on (0, 2); absolute maximum at (4, 6) and(0,2); absolute minimum at (-2, 0) and (2, 0)

Quizplus · Accepted Answer

The function is increasing on the intervals (-2,0) and (2,4) because the slopes of the tangent lines are positive on those intervals. It is decreasing on the interval (0,2) because the slope of the tangent line is negative on that interval.

The absolute maximum occurs at (4,6) because that is the highest point on the graph. The absolute minimum occurs at (-2,0) and (2,0) because those are the lowest points on the graph.

There is also a local maximum at (0,2) because it is the highest point in a small neighborhood around it. However, it is not an absolute maximum because there are points on the graph that are higher.

Find the Open Intervals on Which the Function Is Increasing