First Derivative Test Worksheet
A worksheet for Grade 10 students covering the First Derivative Test, including finding critical points, intervals of increase and decrease, and local extrema.
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First Derivative Test Worksheet
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Read each question carefully and show all your work. Use the First Derivative Test to determine intervals of increase/decrease and local extrema for the given functions.
1. Find the critical points of the function f(x) = x³ - 6x² + 5.
2. For the function f(x) = x² - 4x + 3, the critical point is x = .
At this point, the function has a local (maximum/minimum).
3. Determine the intervals where the function f(x) = x³ - 3x² - 9x + 1 is increasing and decreasing.
4. If f'(x) changes from positive to negative at x = c, what does the First Derivative Test imply about f(x) at x = c?
Local minimum
Local maximum
Inflection point
No extremum
5. The First Derivative Test can be used to find absolute extrema.
True
False
6. Analyze the function f(x) = (x - 2)²(x + 1) using the First Derivative Test to find all local extrema.
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