Question

given the graph of the function f below, determine all intervals on the open interval (-9, 9) where f(x) ≥ 0 and f(x) ≤ 0. f(-8.5)=2.0626

Explanation:

Step1: Recall the meaning of $f^{\prime}(x)\geq0$

A function $y = f(x)$ is non - decreasing when $f^{\prime}(x)\geq0$, which means the graph of the function is going up or is horizontal.

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

The function $y = f(x)$ satisfies $f(x)\leq0$ when the graph of the function is on or below the $x$ - axis.

Step3: Analyze the graph

By looking at the graph of $y = f(x)$ in the open interval $(-9,9)$, we find the intervals where the graph is non - decreasing and on or below the $x$ - axis. The graph is non - decreasing (going up or horizontal) and on or below the $x$ - axis in the interval $(-8,- 7)$.

Answer:

$(-8,-7)$