Question: The graph of $f'$, the derivative of the function $f$, is shown below. Determine all intervals on which $f$ is increasing on the closed interval $[-9, 9]$. Graph of $f'$ at center: a smooth curve starts at the filled point $(-9, -2)$, rises and crosses the x-axis near $x = -8$, reaches a local maximum near $(-4, 5)$, decreases crossing the x-axis near $x = -1$ and stays below the x-axis until rising to cross again near $x = 8$, then continues upward to the filled point $(9, 3)$.

1. **State the problem:** We need to find the intervals on $[-9,9]$ where the function $f$ is increasing. 2. **Recall the rule:** A function $f$ is increasing where its derivative $f'$ is positive (i.e., $f'(x) > 0$). 3. **Analyze the graph of $f'$:** - $f'$ starts negative at $x=-9$. - $f'$ crosses the x-axis near $x=-8$ going from negative to positive. - $f'$ remains positive until it crosses the x-axis again near $x=-1$ going from positive to negative. - $f'$ stays negative until it crosses the x-axis near $x=8$ going from negative to positive. - $f'$ remains positive until $x=9$. 4. **Determine intervals where $f'(x) > 0$:** - From approximately $x=-8$ to $x=-1$. - From approximately $x=8$ to $x=9$. 5. **Write the answer:** $$ \text{Intervals where } f \text{ is increasing: } [-8,-1] \cup [8,9] $$ Note: Since the problem states the closed interval $[-9,9]$, and the graph shows $f'$ crossing the x-axis at these points, we include the endpoints where $f'(x)=0$ as part of the intervals where $f$ is increasing.