Extrema in Calculus
Explore finding local and absolute extrema of functions using derivatives in this Grade 11 Calculus worksheet.
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Extrema in Calculus
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Read each question carefully and provide clear, detailed solutions. Show all your work for full credit.
1. Which of the following conditions guarantees a local extremum at a critical point c?
f'(c) = 0
f''(c) = 0
f'(c) = 0 and f''(c) ≠ 0
f'(c) is undefined
2. A point where the derivative of a function is zero or undefined is called a point.
3. The Theorem states that if a function is continuous on a closed interval [a, b], then it must attain both a maximum and minimum value on that interval.
4. Find the critical points of the function f(x) = x³ - 6x² + 5.
5. A local maximum is always the absolute maximum of a function.
True
False
6. Consider the graph of a function f(x) below. Identify the approximate x-values where local maxima and minima occur.
7. A rectangular box with a square base is to be made from 1200 cm² of material. Find the dimensions of the box that will maximize its volume.