for this question, please note that end - points are considered relative extrema. please use a comma to…

for this question, please note that end - points are considered relative extrema. please use a comma to separate all answers.\nthe ordered pair(s) that represent the relative min is/are:\nthe ordered pair(s) that represent the absolute min is/are:\nthe ordered pair(s) that represent the relative max is/are:\nthe ordered pair(s) that represent the absolute max is/are:\nif there is more than one answer, enter them separated by a comma.\nif there is no answer, enter \dne\\nquestion help: message instructor

for this question, please note that end - points are considered relative extrema. please use a comma to separate all answers.\nthe ordered pair(s) that represent the relative min is/are:\nthe ordered pair(s) that represent the absolute min is/are:\nthe ordered pair(s) that represent the relative max is/are:\nthe ordered pair(s) that represent the absolute max is/are:\nif there is more than one answer, enter them separated by a comma.\nif there is no answer, enter \dne\\nquestion help: message instructor

Answer

Explanation:

Relative Min

A relative minimum is a point where the function changes from decreasing to increasing. Looking at the graph, the point ((1,1)) is a relative minimum. Also, endpoints can be relative extrema. But here, ((0,2)) is higher than ((1,1)) and ((5,0)) is lower but is not a relative minimum (since the function is decreasing before (x = 5)).

Absolute Min

The absolute minimum is the lowest - valued point in the entire domain of the function. Comparing the (y) - values of the points ((0,2)), ((1,1)), ((4,4)), ((5,0)), the (y) - value of (1) at ((1,1)) and (0) at ((5,0)). Since (0<1), the absolute minimum is ((5,0)).

Relative Max

A relative maximum is a point where the function changes from increasing to decreasing. The point ((4,4)) is a relative maximum. Also, endpoints: ((0,2)) is a local maximum (as the function is decreasing just after (x = 0))

Absolute Max

The absolute maximum is the highest - valued point in the entire domain of the function. Comparing the (y) - values of the points ((0,2)), ((1,1)), ((4,4)), ((5,0)), the (y) - value of (4) at ((4,4)) is the highest.

Answer:

The ordered pair(s) that represent the relative min is/are: ((1,1)) The ordered pair(s) that represent the absolute min is/are: ((5,0)) The ordered pair(s) that represent the relative max is/are: ((0,2),(4,4)) The ordered pair(s) that represent the absolute max is/are: ((4,4))