a local maximum of the function f(x) occurs for which x - value?\n| x | f(x) |\n| -4 | 16 |\n| -3 | -2 |\n|…

Explanation:

Step1: Understand local maximum

A local maximum is a point where the function value is greater than the values at nearby points.

Step2: Check function values

We compare the $f(x)$ values for different $x$ - values. When $x=-4$, $f(-4) = 16$; when $x=-3$, $f(-3)=-2$; when $x = - 2$, $f(-2)=0$; when $x=-1$, $f(-1)=6$; when $x = 0$, $f(0)=0$; when $x = 1$, $f(1)=-2$.

Step3: Identify local maximum

The value of $f(x)$ is largest among its neighbors when $x=-1$ since $f(-1)=6$ and the values of $f(x)$ for $x$ values close to $-1$ (like $x=-2$ with $f(-2)=0$ and $x = 0$ with $f(0)=0$) are smaller.

Answer:

-1