Introduction to Derivative Graphs
Explore the relationship between a function's graph and its derivative's graph with this Grade 9 worksheet.
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Introduction to Derivative Graphs
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Read each question carefully and provide clear, concise answers. For graphing questions, draw your graphs neatly on the provided coordinate planes.
1. In your own words, explain what a derivative represents graphically. How does the slope of a tangent line relate to the derivative?
2. Consider a function f(x) whose graph is increasing. What can be said about the sign of its derivative, f'(x), in that interval?
f'(x) > 0 (positive)
f'(x) < 0 (negative)
f'(x) = 0
Cannot be determined
3. If a function f(x) has a local maximum or minimum, its derivative f'(x) will be at that point.
4. When the graph of f(x) is concave up, the graph of f'(x) is .
5. Sketch the graph of the derivative, f'(x), for the given function f(x) shown below.
6. If f'(x) is constant, then the graph of f(x) is a straight line.
True
False