given the graph of the function $f$ below, determine all intervals on the open interval $(-9,9)$ where…

Explanation:

Step1: Understand the meaning of $f'(x)\geq0$

$f'(x)\geq0$ means the function $f(x)$ is non - decreasing, i.e., the slope of the tangent line to the graph of $y = f(x)$ is non - negative. On the graph, this corresponds to the parts where the function is going up or is horizontal (slope = 0).

Step2: Understand the meaning of $f(x)\leq0$

$f(x)\leq0$ means the function values are non - positive, i.e., the graph of the function lies on or below the $x$ - axis.

Step3: Identify the intervals

By looking at the graph, we find the intervals where both conditions are met. The function $f(x)$ is non - decreasing and non - positive in the interval $(-8,-6)$.

Answer:

$(-8,-6)$