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\tf(x)\n-4\t105\n-3\t0\n-2\t-15\n-1\t0\n0\t9\n1\t0\n2\t-15\n3\t0\n4\t105\n5\t384

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\tf(x)\n-4\t105\n-3\t0\n-2\t-15\n-1\t0\n0\t9\n1\t0\n2\t-15\n3\t0\n4\t105\n5\t384

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 table values

We check each $x$ - value and its $y = f(x)$ value. At $x=-2$, $f(-2)=-15$ and at $x = 0$, $f(0)=9$ and at $x=-1$, $f(-1)=0$. Also at $x = 2$, $f(2)=-15$ and the values around it are higher. For example, $f(1) = 0$ and $f(3)=0$.

Answer:

$(2,-15)$