determining a local maximum and minimum analyze the table of values for the continuous function, f(x), to…

determining a local maximum and minimum analyze the table of values for the continuous function, f(x), to complete the statements. a local maximum occurs over the interval a local minimum occurs over the interval x f(x) -3 -16 -2 -1 -1 2 0 -1 1 -4 2 -1

determining a local maximum and minimum analyze the table of values for the continuous function, f(x), to complete the statements. a local maximum occurs over the interval a local minimum occurs over the interval x f(x) -3 -16 -2 -1 -1 2 0 -1 1 -4 2 -1

Answer

Explanation:

Step1: Recall local - max/min definition

A local maximum is a point where the function value is greater than the values at nearby points, and a local minimum is a point where the function value is less than the values at nearby points.

Step2: Analyze the table

We see that (f(-1)=2), and (f(-2)= - 1), (f(0)=-1). Since (2>-1), (x = - 1) is a local maximum. The interval around (x=-1) is ((-2,0)) (open - interval as we are considering local behavior).

Step3: Find local minimum

We see that (f(1)=-4), and (f(0)=-1), (f(2)=-1). Since (-4 < - 1), (x = 1) is a local minimum. The interval around (x = 1) is ((0,2)) (open - interval as we are considering local behavior).

Answer:

A local maximum occurs over the interval ((-2,0)). A local minimum occurs over the interval ((0,2)).