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The problem asks to "Select all values of \(x\) where the function \(f\) has a critical point such that \(f'(x) = 0\)." 

To find where the derivative \(f'(x) = 0\), we need to look at points where the slope of the tangent line to the curve is horizontal (i.e., where the graph has a local maximum, minimum, or a point of inflection with a horizontal tangent).

Looking at the graph, critical points occur where the slope is zero (i.e., flat spots on the curve):

- \(x = -6\) (local minimum)
- \(x = -2\) (local maximum)
- \(x = 3\) (local minimum)
- \(x = 6\) (local maximum)

These are the points where \(f'(x) = 0\). So the correct values of \(x\) are:

- \(x = -6\)
- \(x = -2\)
- \(x = 3\)
- \(x = 6\)

Would you like further clarification on how to identify critical points or explore other related concepts?

Here are 5 related questions to consider:
1. How do you find critical points from the derivative of a function?
2. What is the significance of \(f'(x) = 0\) in calculus?
3. How can you determine if a critical point is a local minimum or maximum?
4. What happens when \(f'(x)\) does not exist at a point but \(f(x)\) is continuous?
5. How does the second derivative test help classify critical points?

**Tip:** Critical points occur where the derivative of a function is zero or undefined, and they are essential for finding local extrema (maximums and minimums).

Select all values of x where the function f has a critical point such that f'(x) = 0.

Learn how to find the critical points of the function f(x) by solving where the derivative f'(x) = 0. This problem covers key calculus concepts such as derivatives, critical points, and local extrema. Suitable for students in Grades 10-12.

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