Question

identify the extrema, increasing, and decreasing: absolute minimum: (0, - 4) relative minimum: (0, - 4) decreasing: (-∞, - 2), (0, ∞) absolute maximum:(-2,0) relative maximum: (-2,0) increasing: (-∞, - 2), (0, ∞)

Explanation:

Step1: Identify relative extrema

Relative extrema occur where the graph changes from increasing to decreasing (relative maximum) or vice - versa (relative minimum). At x = - 2, the graph changes from increasing to decreasing, so (-2,0) is a relative maximum. At x = 0, the graph changes from decreasing to increasing, so (0,-4) is a relative minimum.

Step2: Determine increasing intervals

The function is increasing when the y - values are getting larger as x increases. From the graph, the function is increasing on the interval (-2,0).

Step3: Determine decreasing intervals

The function is decreasing when the y - values are getting smaller as x increases. From the graph, the function is decreasing on (-∞, -2) and (0,∞).

Answer:

• Relative maximum: (-2,0)
• Relative minimum: (0, - 4)
• Increasing: (-2,0)
• Decreasing: (-∞, -2),(0,∞)