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…

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 the values at nearby points.

Step2: Analyze given points

We have the points (-2, -8), (-1, -3), (0, -2), (1, 4), (2, 1), (3, 3).

Step3: Compare function - values

  • At x=-2, f(-2)=-8.
  • At x=-1, f(-1)=-3.
  • At x = 0, f(0)=-2.
  • At x = 1, f(1)=4.
  • At x = 2, f(2)=1.
  • At x = 3, f(3)=3. The smallest function - value among these is f(-2)=-8. But if we consider the options, we need to find the closest local minimum among them. Among the options, the point with the smallest y - value is (0, -2).

Answer:

(0, -2)