Question

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

Explanation:

Step1: Recall definitions

• Relative min: A point where the function changes from decreasing to increasing.
• Absolute min: The lowest point in the entire domain.
• Relative max: A point where the function changes from increasing to decreasing.
• Absolute max: The highest point in the entire domain.

Step2: Analyze the graph

• For relative min: At \(x = 1\), \(y=1\) (since the function changes from decreasing to increasing here).
• For absolute min: The lowest \(y -\)value in the domain \([0,5]\) is \(y = 1\) at \(x = 1\).
• For relative max: At \(x = 4\), \(y = 4\) (since the function changes from increasing to decreasing here).
• For absolute max: The highest \(y -\)value in the domain \([0,5]\) is \(y = 4\) at \(x = 4\).

Answer:

\((1,1)\)
\((1,1)\)
\((4,4)\)
\((4,4)\)