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\n| x | f(x) |\n| -2 | -8 |\n| -1 | -3 |\n| 0 | -2 |\n| 1 | 4 |\n| 2 | 1 |\n| 3 | 3 |

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\n| x | f(x) |\n| -2 | -8 |\n| -1 | -3 |\n| 0 | -2 |\n| 1 | 4 |\n| 2 | 1 |\n| 3 | 3 |

Answer

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 function values

We have the following function - values: $f(-2)=-8$, $f(-1)=-3$, $f(0)=-2$, $f(1)=4$, $f(2)=1$, $f(3)=3$.

Step3: Compare values

Among these values, $f(-2)=-8$ is the smallest. But we need to check if it is a local - minimum. The value of the function at $x = - 1$ is $f(-1)=-3$ which is greater than $f(-2)$. Also, we don't have values for $x$ less than $-2$. So, $(-2,-8)$ is a local minimum.

Answer:

There is no option with $(-2,-8)$. Among the given options, the closest to a local minimum considering the trend of the function values is $(0, - 2)$ as the function value is relatively small compared to its neighbors in the given set of points. So the answer is $(0,-2)$.