Question

A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 16, negative 1, 2, negative 1, negative 4, negative 1. 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

Answer 1

Using the definitions of local maximum and minimum, it is found that:

• There is a local maximum in the interval [-1,0], as the function decreases in the interval.

• There is a local minimum in the interval [1,2], as the function increases in the interval.

Where are there local maximums and minimum on a function?

• When a function changes from increasing to decreasing, there is a local maximum.

• When a function changes from decreasing to increasing, there is a local minimum.

In this problem, we have that the function is as follows:

• f(-3) = -16.

• f(-2) = -1.

• f(-1) = 2.

• f(0) = -1.

• f(1) = -4.

• f(2) = -1.

Hence:

• There is a local maximum in the interval [-1,0], as the function decreases in the interval.

• There is a local minimum in the interval [1,2], as the function increases in the interval.

More can be learned about the maximum and the minimum of a function at brainly.com/question/13539822

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