Derivative Graphs Worksheet
Explore the relationship between functions and their derivatives graphically with this Grade 10 calculus worksheet.
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Derivative Graphs: Grade 10 Calculus
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Read each question carefully and provide your answers. For questions involving graphs, analyze the given graph or sketch your own as instructed.
1. If a function's derivative is positive over an interval, what does this tell you about the original function's behavior in that interval?
2. When the derivative of a function is zero at a point, what does this typically indicate about the original function's graph at that point?
3. Consider a function f(x) whose graph is increasing, then reaches a local maximum, and then decreases. Which of the following best describes the graph of its derivative, f'(x)?
f'(x) is always positive.
f'(x) is always negative.
f'(x) starts positive, crosses the x-axis, then becomes negative.
f'(x) starts negative, crosses the x-axis, then becomes positive.
4. If a function f(x) has a sharp corner, its derivative f'(x) will be undefined at that point.
True
False
5. The graph of a derivative f'(x) shows the slope of the tangent line to the original function f(x) at each point.
True
False
6. For the function f(x) shown below, sketch the graph of its derivative, f'(x), on the provided coordinate plane.
To the left is the graph of f(x) = x^3 - 3x. To the right, sketch the graph of f'(x).
7. If the graph of f'(x) is a horizontal line above the x-axis, what can you conclude about the original function f(x)?