according to the table, which ordered pair is a local minimum of the function, f(x)? (0, 9) (4, 105) (-1, 0)…

Explanation:

Step1: Understand local minimum

A local minimum is a point where the function value is less than or equal to the values of the function at nearby points.

Step2: Analyze table values

We check each (x) - value and its corresponding (f(x)) value and compare with adjacent (f(x)) values. For (x=-4), (f(-4) = 105), and (f(-3)=0), so ((-4,105)) is not a local - minimum. For (x=-3), (f(-3) = 0), (f(-2)=-15), so ((-3,0)) is not a local - minimum. For (x=-2), (f(-2)=-15), (f(-1) = 0), and (f(-2)) is less than (f(-1)) and (f(-3)), but we keep checking. For (x=-1), (f(-1)=0), (f(0)=9), so ((-1,0)) is not a local - minimum. For (x = 0), (f(0)=9), (f(1)=0), so ((0,9)) is not a local - minimum. For (x = 1), (f(1)=0), (f(2)=-15), so ((1,0)) is not a local - minimum. For (x = 2), (f(2)=-15), (f(1)=0) and (f(3)=0). Since (f(2)=-15) is less than (f(1)) and (f(3)), the point ((2,-15)) is a local minimum. For (x = 3), (f(3)=0), (f(4)=105), so ((3,0)) is not a local - minimum. For (x = 4), (f(4)=105), (f(5)=384), so ((4,105)) is not a local - minimum.

Answer:

((2,-15))