Extrema in Calculus Worksheet
A Grade 12 Calculus worksheet focusing on finding and classifying extrema of functions using derivatives.
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Extrema in Calculus
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Read each question carefully and show all your work. Use calculus techniques to find and classify extrema.
1. Find all critical points and classify them as local maxima, local minima, or neither for the function f(x) = x³ - 6x² + 5.
2. What are the absolute maximum and minimum values of the function g(x) = x² - 4x + 1 on the interval [0, 3]?
Max: 1, Min: -3
Max: 1, Min: -2
Max: 3, Min: -2
Max: 3, Min: -3
3. If f'(x) changes from positive to negative at x = c, then f has a local at x = c.
4. If f'(x) changes from negative to positive at x = c, then f has a local at x = c.
5. Use the Second Derivative Test to classify the critical points of f(x) = x⁴ - 8x².
6. A function can have an absolute maximum or minimum at a point where its derivative is undefined.
True
False
7. A rectangular box with a square base and no top is to be made from 1200 cm² of material. Find the dimensions of the box that will maximize its volume.