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…

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)\n\nx\tf(x)\n-2\t-8\n-1\t-3\n0\t-2\n1\t4\n2\t1\n3\t3

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)\n\nx\tf(x)\n-2\t-8\n-1\t-3\n0\t-2\n1\t4\n2\t1\n3\t3

Answer

Explanation:

Step1: Understand local minimum

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

Step2: Analyze the table values

We have the following points: (-2,-8), (-1,-3), (0,-2), (1,4), (2,1), (3,3). The value of the function at x = - 2 is -8, at x=-1 is -3, at x = 0 is -2, at x = 1 is 4, at x = 2 is 1 and at x = 3 is 3.

Step3: Compare function values

We see that the function value at x = 0 is -2. Among the given points, the function value at x=-2 is -8 which is lower but we are looking for the closest local - minimum among the given options. The value of the function at x = 0 is lower than the values at x=-1 and x = 1.

Answer:

(0, -2)