according to the table, which ordered pair is a local maximum of the function, f(x)?\no (0, 64)\no (3…

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 table values

Check each $x$ - value and its corresponding $f(x)$ value and compare with adjacent $f(x)$ values. When $x = - 2$, $f(-2)=0$, $f(-1) = 45>f(-2)$. When $x=-1$, $f(-1) = 45$, $f(0)=64 > f(-1)$. When $x = 0$, $f(0)=64$, $f(1)=45<f(0)$. When $x = 1$, $f(1)=45$, $f(2)=0<f(1)$. When $x = 2$, $f(2)=0$, $f(3)=-35<f(2)$. When $x = 3$, $f(3)=-35$, $f(4)=0>f(3)$. When $x = 4$, $f(4)=0$, $f(5)=189>f(4)$. When $x = 5$, $f(5)=189$, $f(6)=640>f(5)$. The function value $f(0) = 64$ is greater than the function - values at the adjacent $x$ - values ($x=-1$ and $x = 1$).

Answer:

A. $(0,64)$