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

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.\na. the local maximum of ( y = f(x) ) is ( f(2)=4 ).\n(type integers or simplified fractions.)\nb. there are two local maxima. the leftmost maximum is ( f()= ) the rightmost maximum is and ( f()= ).\n(type integers or simplified fractions.)\nc. there is no local maximum for ( y = f(x) ).\nselect the correct answer and, if necessary, fill in the answer boxes to complete your choice.\na. the local minimum of ( y = f(x) ) is ( f()= ).\n(type integers or simplified fractions.)\nb. there are two local minima. the leftmost minimum is ( f()= ) and the rightmost minimum is ( f()= ).\n(type integers or simplified fractions.)\nc. there is no local minimum 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.\na. the local maximum of ( y = f(x) ) is ( f(2)=4 ).\n(type integers or simplified fractions.)\nb. there are two local maxima. the leftmost maximum is ( f()= ) the rightmost maximum is and ( f()= ).\n(type integers or simplified fractions.)\nc. there is no local maximum for ( y = f(x) ).\nselect the correct answer and, if necessary, fill in the answer boxes to complete your choice.\na. the local minimum of ( y = f(x) ) is ( f()= ).\n(type integers or simplified fractions.)\nb. there are two local minima. the leftmost minimum is ( f()= ) and the rightmost minimum is ( f()= ).\n(type integers or simplified fractions.)\nc. there is no local minimum for ( y = f(x) ).

Answer

Explanation:

Step1: Analyze local maxima

A local maximum is a point where the function changes from increasing to decreasing. Looking at the graph, at (x = 2), the function (y = f(x)) has a local maximum. The value of the function at (x=2) is (y = f(2)=4). There is no other point where the function changes from increasing to decreasing. So option A for local maxima is correct.

Step2: Analyze local minima

A local minimum is a point where the function changes from decreasing to increasing. At (x = 0), the function (y=f(x)) has a local minimum ((y = f(0)=1)). At (x = 4), the function also has a local minimum ((y = f(4)=3)). So for local minima, option B is correct. The left - most local minimum is at (x = 0) with (f(0)=1) and the right - most local minimum is at (x = 4) with (f(4)=3).

Answer:

For local maxima: A. The local maximum of (y = f(x)) is (f(2)=4). For local minima: B. There are two local minima. The leftmost minimum is (f(0)=1) and the rightmost minimum is (f(4)=3).