predicting key aspects using a table\nwhich interval contains a local maximum for this function?\nwhich…

Explanation:

Step1: Understand local maximum

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

Step2: Analyze the table

We check the $f(x)$ - values. At $x=-1$, $f(-1) = 0$. Before $x=-1$ ($x = - 2$, $f(-2)=-4$) and after $x=-1$ ($x = 0$, $f(0)=-2$), the function - values are smaller. So, the function has a local maximum in the interval $(-2,0)$.

Step3: Understand local minimum

A local minimum is a point where the function value is less than the values at neighboring points.

Step4: Analyze the table for local minimum

At $x = 0$, $f(0)=-2$. Before $x = 0$ ($x=-1$, $f(-1) = 0$) and after $x = 0$ ($x = 1$, $f(1)=-4$), the function - values are larger. So, the function has a local minimum in the interval $(-1,1)$.

Answer:

Local maximum interval: $(-2,0)$ Local minimum interval: $(-1,1)$