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

Answer

Explanation:

Step1: Recall the definition of local maximum

A local maximum is a point where the function value is greater than or equal to the values of the function in the neighboring points.

Step2: Analyze the given points

We have points ((1,5)), ((2,3)), ((3,4)), ((4,1)). At (x = 1), the function value (y=f(1)=5). At (x = 3), the function value (y = f(3)=4). Since (5>4) and (5) is greater than the values of the function in the neighborhood of (x = 1) (for example, near (x=1), as (x) moves from (0) to (2), the function first has a value at (x = 1) and then decreases to (x=2)), and (4) is greater than the values of the function in the neighborhood of (x = 3) (as (x) moves from (2) to (4), the function first increases to (x = 3) and then decreases to (x=4)).

Answer:

B. The local maxima of (y = f(x)) are (f(1)=5) and (f(3)=4)