https://file.aiquickdraw.com/mathbot/file/1727047693014gyyjpmw2.jpg

The image above represents the derivative \( f'(x) \) based on the given graph of \( f(x) \). It highlights the key points where the slopes change and matches the increasing and decreasing sections of the original function \( f(x) \).

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Here are 5 related questions to extend your understanding:
1. How does the derivative behave at sharp corners or cusps in a graph?
2. What is the relationship between a positive slope in \( f(x) \) and the value of \( f'(x) \)?
3. Can you identify which sections of \( f(x) \) correspond to zero slope (horizontal tangent)?
4. How do changes in concavity of \( f(x) \) affect the second derivative, \( f''(x) \)?
5. How does the graph of \( f'(x) \) change when \( f(x) \) has a parabolic shape?

**Tip**: The derivative \( f'(x) \) is always positive where the original function \( f(x) \) is increasing and negative where \( f(x) \) is decreasing.

Given the graph of a function f(x), sketch the graph of its derivative f'(x).

Analyze the graph of a piecewise linear function f(x) and sketch the corresponding graph of its derivative f'(x). This problem covers key calculus concepts, focusing on slope analysis and graphical interpretation of derivatives. Suitable for high school and college-level calculus students.

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