Question

question
given the graph of the function f below, determine all intervals on the open interval (-9,9)
where f(x) ≥ 0.

Explanation:

Step1: Recall the relationship between \(f^{\prime}(x)\) and the function \(f(x)\)

If \(f^{\prime}(x)>0\) on an open interval \(I\), then the function \(y = f(x)\) is increasing on the interval \(I\).

Step2: Analyze the graph

Looking at the graph of \(y = f(x)\), we observe the intervals where the function is increasing.
From the graph, we can see that the function \(f(x)\) is increasing on the intervals \((-9,-5)\) and \((-1,7)\)

Answer:

The function \(f(x)\) is increasing (where \(f^{\prime}(x)>0\)) on the intervals \((-9, - 5)\) and \((-1,7)\)