To determine where $f'(x) = 0$, we need to identify the points where the slope of the function $f(x)$ is zero. These are points where the graph of $f(x)$ has horizontal tangents, meaning it either reaches a local maximum or minimum.

From the graph description:

• The function has a minimum at $(4, 3)$.

At this point, the graph is flat (the tangent line is horizontal), so the derivative $f'(x) = 0$ at $x = 4$.

Thus, the correct answer is:

A. The x-value where $f'(x) = 0$ is $x = 4$.

Would you like further clarification or details on any part?

Here are 5 additional questions related to this concept:

1. What does the derivative $f'(x)$ represent graphically?
2. How do local maxima and minima relate to the derivative of a function?
3. What is the second derivative test, and how does it apply to points where $f'(x) = 0$?
4. Can a point where $f'(x) = 0$ also be an inflection point?
5. How would you calculate $f'(x)$ from a given function algebraically?

Tip: The points where $f'(x) = 0$ often indicate key features like maxima, minima, or critical points.