Question

A 2-column table with 10 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, 4, 5. The second column is labeled f of x with entries 105, 0, negative 15, 0, 9, 0, negative 15, 0, 105, 384.

According to the table, which ordered pair is a local minimum of the function, f(x)?
(0, 9)
(4, 105)
(–1, 0)
(2, –15)

Answer 1

D

Explanation:

Answer 2

To determine which ordered pair is a local minimum of the function, f(x), we need to look for a point where the function value is smaller than the values of the function at the surrounding points.

From the table, we can see that the function value at x = 2 is -15, which is smaller than the function values at x = 1 and x = 3, which are both 0. Therefore, the ordered pair (2, -15) is a local minimum of the function, f(x).

Note that the ordered pairs (0, 9), (4, 105), and (-1, 0) are not local minima, as the function values at these points are all larger than the values at their surrounding points.