determine all x - values for which the graph of f has a horizontal tangent line on the closed interval -9,9.

Explanation:

Step1: Recall tangent - slope relationship

The slope of the tangent line to the graph of $y = f(x)$ is given by $f'(x)$. A horizontal tangent line has a slope of 0, so we need to find where $f'(x)=0$.

Step2: Analyze the graph

Visually inspect the graph of $y = f(x)$ on the interval $[-9,9]$. The graph has horizontal tangent lines at the local maxima and minima. From the graph, we can see that the function has horizontal tangent lines at $x=-6$ and $x = 3$.

Answer:

$x=-6,3$