Question

below is the graph of a function f(x). identify all relative extrema and absolute extrema. (type ordered pairs. if you have more than one answer, separate them by commas.) (you can click on a graph to enlarge it.) absolute maximum: absolute minimum: relative maximum(s): relative minimum(s):

Explanation:

Step1: Define relative and absolute extrema

Relative extrema are local maximum or minimum points. Absolute extrema are the overall maximum and minimum points on the domain shown.

Step2: Identify absolute maximum

The highest point on the graph in the given domain is at approximately $(6.5, 7.5)$. So the absolute maximum is $(6.5, 7.5)$.

Step3: Identify absolute minimum

The lowest point on the graph in the given domain is at approximately $(8.5,-6)$. So the absolute minimum is $(8.5,-6)$.

Step4: Identify relative maximums

Relative maximums occur where the graph changes from increasing to decreasing. These points are approximately $(- 5,6)$ and $(1,3)$. So the relative maximums are $(-5,6),(1,3)$.

Step5: Identify relative minimums

Relative minimums occur where the graph changes from decreasing to increasing. These points are approximately $(-2.5,-0.5)$ and $(2,-4)$. So the relative minimums are $(-2.5,-0.5),(2,-4)$.

Answer:

Absolute maximum: $(6.5, 7.5)$
Absolute minimum: $(8.5,-6)$
Relative maximum(s): $(-5,6),(1,3)$
Relative minimum(s): $(-2.5,-0.5),(2,-4)$