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

according to the table, which ordered pair is a local minimum of the function, f(x)?\n(0, 9)\n(4, 105)\n(-1, 0)\n(2, -15)\n\nx f(x)\n-4 105\n-3 0\n-2 -15\n-1 0\n0 9\n1 0\n2 -15\n3 0\n4 105\n5 384

according to the table, which ordered pair is a local minimum of the function, f(x)?\n(0, 9)\n(4, 105)\n(-1, 0)\n(2, -15)\n\nx f(x)\n-4 105\n-3 0\n-2 -15\n-1 0\n0 9\n1 0\n2 -15\n3 0\n4 105\n5 384

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 the table values

We check the $f(x)$ - values for each $x$. At $x = - 2$, $f(-2)=-15$ and at $x = 0$, $f(0) = 9$. Also, at $x=1$, $f(1)=0$. But at $x = 2$, $f(2)=-15$. The value of the function at $x = 2$ is less than the values of the function at nearby $x$ - values ($x = 1$ and $x = 3$ where $f(1)=0$ and $f(3)=0$).

Answer:

$(2,-15)$