question 2 of 7 consider the graph of the function y = f(x) on the closed interval x1, x9. classify each of…

question 2 of 7 consider the graph of the function y = f(x) on the closed interval x1, x9. classify each of the nine points as the absolute maximum, the absolute minimum, a relative maximum, a relative minimum, or none. if a point is both a relative and an absolute extremum, then identify it as the absolute extremum. answer bank relative minimum absolute minimum none absolute maximum relative maximum

question 2 of 7 consider the graph of the function y = f(x) on the closed interval x1, x9. classify each of the nine points as the absolute maximum, the absolute minimum, a relative maximum, a relative minimum, or none. if a point is both a relative and an absolute extremum, then identify it as the absolute extremum. answer bank relative minimum absolute minimum none absolute maximum relative maximum

Answer

Explanation:

Step1: Recall definitions

An absolute maximum is the highest - value of the function on the entire interval, an absolute minimum is the lowest - value. A relative maximum is a point where the function value is greater than the values of the function at nearby points, and a relative minimum is a point where the function value is less than the values of the function at nearby points.

Step2: Analyze (x_1)

The function value at (x_1) is not the highest or lowest on the interval and is not a local extremum. So it is none.

Step3: Analyze (x_2)

The function value at (x_2) is higher than the values at nearby points, so it is a relative maximum.

Step4: Analyze (x_3)

The function value at (x_3) is not the highest or lowest on the interval and is not a local extremum. So it is none.

Step5: Analyze (x_4)

The function value at (x_4) is lower than the values at nearby points, so it is a relative minimum.

Step6: Analyze (x_5)

The function value at (x_5) is not the highest or lowest on the interval and is not a local extremum. So it is none.

Step7: Analyze (x_6)

The function value at (x_6) is higher than the values at nearby points, so it is a relative maximum.

Step8: Analyze (x_7)

The function value at (x_7) is not the highest or lowest on the interval and is not a local extremum. So it is none.

Step9: Analyze (x_8)

The function value at (x_8) is lower than the values at nearby points, so it is a relative minimum.

Step10: Analyze (x_9)

The function value at (x_9) is the lowest value on the entire interval ([x_1,x_9]), so it is the absolute minimum.

Answer:

(x_1): none (x_2): relative maximum (x_3): none (x_4): relative minimum (x_5): none (x_6): relative maximum (x_7): none (x_8): relative minimum (x_9): absolute minimum