Derivative Graphs Worksheet
Understand and interpret derivative graphs, their relationship to original functions, and key features like critical points, concavity, and inflection points.
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Derivative Graphs Worksheet
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Read each question carefully and provide your answer in the space provided. Show all your work for full credit.
1. If the graph of f'(x) is positive, what can be said about the graph of f(x)?
f(x) is decreasing
f(x) is increasing
f(x) is concave up
f(x) is concave down
2. A critical point of f(x) occurs when f'(x) is equal to:
1
0
A positive value
A negative value
3. If f''(x) > 0, then the graph of f(x) is .
4. A point of inflection occurs when the sign of changes.
5. The graph of f'(x) is shown below. On what intervals is f(x) increasing? Explain your reasoning.
6. If f'(x) has a local maximum, then f(x) has an inflection point.
True
False