use the graph of a function y = f(x) to find the absolute maximum and the absolute minimum, if they exist…

use the graph of a function y = f(x) to find the absolute maximum and the absolute minimum, if they exist. identify any local maximum values or local minimum values.\nselect the correct answer and, if necessary, fill in the answer boxes to complete your choice.\na. the absolute maximum of y = f(x) is f( ) = \n(type integers or simplified fractions.)\nb. there is no absolute maximum for y = f(x).

use the graph of a function y = f(x) to find the absolute maximum and the absolute minimum, if they exist. identify any local maximum values or local minimum values.\nselect the correct answer and, if necessary, fill in the answer boxes to complete your choice.\na. the absolute maximum of y = f(x) is f( ) = \n(type integers or simplified fractions.)\nb. there is no absolute maximum for y = f(x).

Answer

Explanation:

Step1: Analyze the graph

The graph has a highest - point and lowest - point in the given domain.

Step2: Identify the absolute maximum

The highest point on the graph in the visible domain is at the point $(2,6)$. So the absolute maximum value of the function $y = f(x)$ occurs when $x = 2$ and $y=f(2)=6$.

Step3: Identify the absolute minimum

The lowest point on the graph in the visible domain is at the point $(0,0)$. So the absolute minimum value of the function $y = f(x)$ occurs when $x = 0$ and $y = f(0)=0$.

Step4: Identify local maxima/minima

A local maximum occurs at a point where the function changes from increasing to decreasing. Here, $(2,6)$ is a local maximum. A local minimum occurs at a point where the function changes from decreasing to increasing. Here, $(4,4)$ is a local minimum.

Answer:

A. The absolute maximum of $y = f(x)$ is $f(2)=6$. The absolute minimum of $y = f(x)$ is $f(0)=0$. Local maximum value: $f(2)=6$. Local minimum value: $f(4)=4$.