Question

question given the graph of the function $f$ below, determine all intervals on the open interval $(-9,9)$ where $f(x)geq0$ and $f(x)leq0$. $f(-8.5)= - 2.0626$ graph of $f$

Explanation:

Step1: Recall derivative - function relationship

If \(f^{\prime}(x)\geq0\), the function \(f(x)\) is non - decreasing.

Step2: Identify non - decreasing intervals

From the graph, we observe the intervals where the function is non - decreasing (slope is non - negative). These are the intervals where the graph is going up or is horizontal.

Step3: Identify non - positive function values

We also need to find where \(f(x)\leq0\), i.e., the part of the graph that lies on or below the \(x\) - axis.

Step4: Combine the two conditions

By looking at the graph, we find the intersection of the non - decreasing intervals and the non - positive intervals on the open interval \((-9,9)\).

Answer:

\((-2,1)\cup(6,9)\)