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

Answer

Explanation:

Step1: Recall the definition of local minimum

A local minimum of a function (y = f(x)) is a point ((a,f(a))) such that (f(a)\leq f(x)) for all (x) in some open interval containing (a).

Step2: Analyze the graph

Looking at the graph of (y = f(x)), we have two points that satisfy the local - minimum condition.

  • For the point ((-1,2)): In an open interval around (x=-1), the value of (y = f(-1)=2) is less than the (y) - values of the function for other (x) values in that interval.
  • For the point ((0,1)): In an open interval around (x = 0), the value of (y=f(0)=1) is less than the (y) - values of the function for other (x) values in that interval.

Answer:

B. There are two local minima. The leftmost minimum is (f(-1)=2) and the rightmost minimum is (f(0)=1)