First Derivative Test Worksheet
A Grade 12 Calculus worksheet focusing on applying the First Derivative Test to determine increasing/decreasing intervals and local extrema of functions.
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First Derivative Test
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Read each question carefully and show all your work. Use the First Derivative Test to determine the intervals where the function is increasing or decreasing, and to find any local maximum or minimum values.
1. Find the critical numbers of the function \(f(x) = x^3 - 6x^2 + 5\).
2. For the function \(f(x) = x^3 - 6x^2 + 5\), determine the intervals on which \(f\) is increasing or decreasing. Illustrate with a number line.
3. Find the local maximum and minimum values of the function \(f(x) = x^3 - 6x^2 + 5\).
4. Analyze the function \(g(x) = x^4 - 4x^3\) using the First Derivative Test to find intervals of increase/decrease and local extrema.
5. If \(f'(c) = 0\), then \(f\) must have a local maximum or minimum at \(x = c\).
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