for the function shown in the graph, list the intervals on which the function is increasing, the intervals…

for the function shown in the graph, list the intervals on which the function is increasing, the intervals on which it is decreasing, and the location of all local extrema. a. the function is decreasing on the interval(s) (type your answer in interval notation. use a comma to separate answers as needed.) b. the function is never decreasing. identify any local extrema. select the correct answer below and, if necessary, fill in any answer box(es) within your choice. a. there is no local maximum, and the local minimum/minima occur(s) at x = (use a comma to separate answers as needed.) b. there is no local minimum, and the local maximum/maxima occur(s) at x = (use a comma to separate answers as needed.) c. there is/are local maximum/maxima x = , and there is/are local minimum/minima at x = (use a comma to separate answers as needed.) d. the function has no local extrema.

for the function shown in the graph, list the intervals on which the function is increasing, the intervals on which it is decreasing, and the location of all local extrema. a. the function is decreasing on the interval(s) (type your answer in interval notation. use a comma to separate answers as needed.) b. the function is never decreasing. identify any local extrema. select the correct answer below and, if necessary, fill in any answer box(es) within your choice. a. there is no local maximum, and the local minimum/minima occur(s) at x = (use a comma to separate answers as needed.) b. there is no local minimum, and the local maximum/maxima occur(s) at x = (use a comma to separate answers as needed.) c. there is/are local maximum/maxima x = , and there is/are local minimum/minima at x = (use a comma to separate answers as needed.) d. the function has no local extrema.

Answer

Explanation:

Step1: Determine increasing intervals

A function is increasing when the graph goes up as we move from left - to - right. From the graph, the function is increasing on the interval $(-8,0)$.

Step2: Determine decreasing intervals

A function is decreasing when the graph goes down as we move from left - to - right. From the graph, the function is decreasing on the interval $(0,4)$.

Step3: Identify local extrema

A local maximum occurs where the function changes from increasing to decreasing. Here, at $x = 0$, the function changes from increasing to decreasing, so there is a local maximum at $x=0$. There are no local minima.

Answer:

  1. Increasing interval: $(-8,0)$
  2. Decreasing interval: $(0,4)$
  3. Local extrema:
    • There is no local minimum, and the local maximum occurs at $x = 0$. So the answer for local extrema is B. There is no local minimum, and the local maximum/maxima occur(s) at $x = 0$.