relative min: absolute min: relative max: absolute max: round your answer(s) to the nearest tenth. if there…

Explanation:

Step1: Define relative extrema

Relative minimum is a point where the function changes from decreasing to increasing. Relative maximum is a point where the function changes from increasing to decreasing.

Step2: Identify relative min

At $x = 2$, the function changes from decreasing to increasing. So the relative - min is $y = 2$.

Step3: Identify absolute min

We compare all the $y$ - values of the points. Among $(1,4),(2,2),(3,3),(5,1)$, the smallest $y$ - value is $y = 1$ at $x = 5$. So the absolute min is $y = 1$.

Step4: Identify relative max

At $x = 1$ and $x = 3$, the function changes from increasing to decreasing. So the relative max values are $y = 4$ at $x = 1$ and $y = 3$ at $x = 3$.

Step5: Identify absolute max

Among the $y$ - values, the largest is $y = 4$ at $x = 1$. So the absolute max is $y = 4$.

Answer:

relative min: 2 absolute min: 1 relative max: 4,3 absolute max: 4