use the graph to identify the points on the interval a,b at which local and absolute extreme values occur…

use the graph to identify the points on the interval a,b at which local and absolute extreme values occur. list the x - values of the points where local minima occur, if any. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the local minimum point(s) occur(s) at x = q (use a comma to separate answers as needed.) b. there are no local minima. list the x - values of the points where local maxima occur, if any. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the local maximum point(s) occur(s) at x = p,r (use a comma to separate answers as needed.) b. there are no local maxima. list the x - values of the points where absolute minima occur, if any. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the absolute minimum point(s) occur(s) at x = b (use a comma to separate answers as needed.) b. there are no absolute minima. list the x - values of the points where absolute maxima occur, if any. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the absolute maximum point(s) occur(s) at x = a (use a comma to separate answers as needed.) b. there are no absolute maxima

use the graph to identify the points on the interval a,b at which local and absolute extreme values occur. list the x - values of the points where local minima occur, if any. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the local minimum point(s) occur(s) at x = q (use a comma to separate answers as needed.) b. there are no local minima. list the x - values of the points where local maxima occur, if any. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the local maximum point(s) occur(s) at x = p,r (use a comma to separate answers as needed.) b. there are no local maxima. list the x - values of the points where absolute minima occur, if any. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the absolute minimum point(s) occur(s) at x = b (use a comma to separate answers as needed.) b. there are no absolute minima. list the x - values of the points where absolute maxima occur, if any. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the absolute maximum point(s) occur(s) at x = a (use a comma to separate answers as needed.) b. there are no absolute maxima

Answer

Explanation:

Step1: Identify local minima

Local minima occur where the function changes from decreasing to increasing. From the graph, this happens at $x = q$.

Step2: Identify local maxima

Local maxima occur where the function changes from increasing to decreasing. From the graph, this happens at $x = p,r$.

Step3: Identify absolute minima

The absolute minimum is the lowest - point on the entire interval $[a,b]$. From the graph, it occurs at $x = b$.

Step4: Identify absolute maxima

The absolute maximum is the highest - point on the entire interval $[a,b]$. From the graph, it occurs at $x = a$.

Answer:

  1. A. The local minimum point(s) occur(s) at $x = q$
  2. A. The local maximum point(s) occur(s) at $x = p,r$
  3. A. The absolute minimum point(s) occur(s) at $x = b$
  4. A. The absolute maximum point(s) occur(s) at $x = a$