To solve this problem, let's analyze the graph provided:

The graph represents the derivative $y = f'(x)$ of a function $f(x)$. To find the critical points of the original function $f(x)$, we need to identify where $f'(x) = 0$ because critical points occur where the derivative of $f(x)$ is zero or undefined. These points correspond to where the graph of $f'(x)$ intersects the x-axis.

Upon examining the graph:

1. The graph of $f'(x)$ intersects the x-axis in two places, indicating two points where $f'(x) = 0$.
2. Each of these intersections represents a critical point for the function $f(x)$, as the slope of $f(x)$ is zero at these points.

Therefore, the original function $f(x)$ has 2 critical points on the interval shown.

Would you like further details or have any questions?

Here are five related questions that expand on this concept:

1. What is the significance of the sign of $f'(x)$ in determining the behavior of $f(x)$?
2. How do you determine whether each critical point is a maximum, minimum, or saddle point?
3. What would be the effect if $f'(x)$ had a vertical asymptote instead of crossing the x-axis?
4. How do we find inflection points of $f(x)$ using its second derivative $f''(x)$?
5. What information about $f(x)$ can be derived from the regions where $f'(x)$ is positive or negative?

Tip: Remember, the critical points are where the derivative equals zero or is undefined. Always check these points to understand the behavior of the function.