https://file.aiquickdraw.com/mathbot/file/172990014580814b12imf.jpg

To find the points where \( f'(x) = 0 \) on the given graph, we need to locate the points where the slope of the curve is zero. These points correspond to the local maxima, minima, or inflection points of the function, where the tangent line is horizontal.

From examining the graph, here’s how to approach it:

1. **Identify Horizontal Tangents**: Look for points where the curve levels out momentarily, showing no upward or downward slope.
2. **Approximate the x-values**: Based on the graph, these horizontal tangent points appear to occur around:
   - \( x \approx -5 \): This seems to be a local maximum.
   - \( x \approx -2 \): This point is a local minimum.
   - \( x \approx 3 \): This looks like a local minimum.

3. **Verify with Context**: Since this is a visual approximation, these points represent places where \( f'(x) = 0 \). 

Would you like further details on how to analytically determine these points or more information on related concepts?

### Related Questions
1. How do you determine \( f(x) \) values if only \( f'(x) = 0 \) points are given?
2. What is the significance of \( f'(x) = 0 \) in analyzing a function's graph?
3. Can points where \( f'(x) = 0 \) always indicate a local maximum or minimum?
4. How would you find inflection points in a similar graph?
5. What does \( f'(x) \neq 0 \) tell you about the graph’s behavior?

**Tip**: When looking for \( f'(x) = 0 \), remember that these points may correspond to local extrema, but also check the curve's concavity to confirm whether it's a max, min, or saddle point.

How can you find the f'(x) = 0 for the given graph?

Learn how to find points where f'(x) = 0 by identifying horizontal tangents on a function graph. Explore calculus concepts, including derivatives and critical points, to understand maxima and minima for grades 11-12.

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