To solve the given problem based on the graph provided, we need to analyze the behavior of the function $f(x)$ and its derivative $f'(x)$ at specific points. I'll walk through each part:

For $f(x)$:

1. (a) $f(-2)$:

   • At $x = -2$, the graph shows the function value $f(x)$ is slightly below 0.
   • Answer: Negative.

2. (b) $f(0)$:

   • At $x = 0$, the graph crosses the x-axis at $f(0) = 0$.
   • Answer: Zero.

3. (c) $f(4)$:

   • At $x = 4$, the function value $f(4)$ is positive, as it is above the x-axis.
   • Answer: Positive.

4. (d) $f(5)$:

   • At $x = 5$, the graph shows $f(5)$ is negative, below the x-axis.
   • Answer: Negative.

For $f'(x)$ (Slope of the graph):

5. (e) $f'(-2)$:

   • At $x = -2$, the slope is positive as the function is increasing.
   • Answer: Positive.

6. (f) $f'(2)$:

   • At $x = 2$, the slope is zero as it is the turning point (maximum point on the graph).
   • Answer: Zero.

7. (g) $f'(4)$:

   • At $x = 4$, the slope is negative as the function is decreasing.
   • Answer: Negative.

8. (h) $f'(5)$:

   • At $x = 5$, the slope is positive as the function starts increasing again.
   • Answer: Positive.

Would you like further details on any specific part? Here are five related questions:

1. How do you determine the sign of the derivative using a graph?
2. Why does the derivative equal zero at a turning point?
3. Can a function's value be negative while its slope is positive? How?
4. What happens to the slope of a function as you move past a local minimum or maximum?
5. How would you interpret the second derivative based on a graph?

Tip: Remember, when analyzing $f'(x)$, you're checking the slope of the tangent line at each point!