according to the table, which ordered pair is a local maximum of the function, f(x)?\no (0, 64)\no (3…
according to the table, which ordered pair is a local maximum of the function, f(x)?\no (0, 64)\no (3, -35)\no (5, 189)\no (2, 0)\n\nx\tf(x)\n-2\t0\n-1\t45\n0\t64\n1\t45\n2\t0\n3\t-35\n4\t0\n5\t189\n6\t640
Answer
Explanation:
Step1: Understand local maximum
A local maximum is a point where the function value is greater than the values at nearby points.
Step2: Analyze the table
We check the $f(x)$ - values around each $x$ - value. For $x=-2$, $f(-2) = 0$, and $f(-1)=45>0$. For $x = - 1$, $f(-1)=45$, and $f(0)=64>45$. For $x = 0$, $f(0)=64$, $f(-1)=45<64$ and $f(1)=45<64$. For $x = 1$, $f(1)=45$, and $f(2)=0<45$. For $x = 2$, $f(2)=0$, and $f(3)=-35<0$. For $x = 3$, $f(3)=-35$, and $f(4)=0>-35$. For $x = 4$, $f(4)=0$, and $f(5)=189>0$. For $x = 5$, $f(5)=189$, and $f(6)=640>189$.
Answer:
A. $(0,64)$