the graph of f, the derivative of the function f, is shown below. determine all intervals on which f(x) < 0…

the graph of f, the derivative of the function f, is shown below. determine all intervals on which f(x) < 0 on the open interval (-9,9).

the graph of f, the derivative of the function f, is shown below. determine all intervals on which f(x) < 0 on the open interval (-9,9).

Answer

Explanation:

Step1: Recall the relationship

The second - derivative $f''(x)$ is the derivative of $f'(x)$. When $f''(x)<0$, the function $f'(x)$ is decreasing.

Step2: Analyze the graph of $f'(x)$

By observing the graph of $y = f'(x)$ on the interval $(-9,9)$, we look for the intervals where the graph of $f'(x)$ is going down - ward. We can see that the graph of $f'(x)$ is decreasing on the intervals $(-9,-2)$ and $(2,8)$.

Answer:

$(-9,-2)\cup(2,8)$