question 18 of 19 this quiz: 95 point(s) possible this question: 5 point(s) possible submit quiz identify…

question 18 of 19 this quiz: 95 point(s) possible this question: 5 point(s) possible submit quiz identify any relative maxima or minima, and intervals on which the function is decreasing and increasing. the relative maximum is at x = the relative minimum is at x = on which intervals is the function increasing? a. (-∞, 2) and (4, 6) b. (2, 6) and (6, ∞) c. (-∞, 2) and (6, ∞) d. (2, -1) and (6, -9) on which interval is the function decreasing? a. (-∞, 2) b. (6, ∞) c. (2, -1) d. (2, 6)

question 18 of 19 this quiz: 95 point(s) possible this question: 5 point(s) possible submit quiz identify any relative maxima or minima, and intervals on which the function is decreasing and increasing. the relative maximum is at x = the relative minimum is at x = on which intervals is the function increasing? a. (-∞, 2) and (4, 6) b. (2, 6) and (6, ∞) c. (-∞, 2) and (6, ∞) d. (2, -1) and (6, -9) on which interval is the function decreasing? a. (-∞, 2) b. (6, ∞) c. (2, -1) d. (2, 6)

Answer

Explanation:

Step1: Recall function behavior concepts

A relative maximum occurs where the function changes from increasing to decreasing. A relative minimum occurs where the function changes from decreasing to increasing. The function is increasing when the y - values increase as x increases and decreasing when y - values decrease as x increases.

Step2: Analyze the graph

Looking at the graph, we can see that the function has a relative maximum at the point (2,3). So the relative maximum is 3 at x = 2.

Step3: Find the relative minimum

The function has a relative minimum at the point (6, - 1). So the relative minimum is - 1 at x = 6.

Step4: Determine increasing intervals

The function is increasing when moving from left - to - right and the y - values are getting larger. The function is increasing on the intervals $(-\infty,2)$ and $(6,\infty)$.

Step5: Determine decreasing intervals

The function is decreasing when moving from left - to - right and the y - values are getting smaller. The function is decreasing on the interval $(2,6)$.

Answer:

The relative maximum is 3 at x = 2. The relative minimum is - 1 at x = 6. On which intervals is the function increasing? C. $(-\infty,2)$ and $(6,\infty)$ On which interval is the function decreasing? D. $(2,6)$