what ordered pair is closest to a local minimum of the function, f(x)?\n(-1,-3)\n(0,-2)\n(1,4)\n(2,1)

Answer:

(0, -2)

Explanation:

Step1: Understand local minimum

A local minimum is a point where the function value is less than the values at neighboring points.

Step2: Analyze given points

For (x=-2), (f(-2)= - 8); for (x = - 1), (f(-1)=-3); for (x = 0), (f(0)=-2); for (x = 1), (f(1)=4); for (x = 2), (f(2)=1); for (x = 3), (f(3)=3).

Step3: Compare function - values

We see that (f(0)=-2) is less than (f(-1)=-3) and (f(1)=4). Among the given points, the function value at (x = 0) is a local minimum compared to its immediate neighbors. So the ordered - pair closest to a local minimum is ((0,-2)).