Applications of Derivatives · Curve Analysis
Critical Points
Critical points occur where the derivative is zero or undefined. These are candidates for local extrema.
- 0 variables
- 2 worked examples
- 15 in Applications of Derivatives
Worked examples
Find the critical points of f(x) = x³ - 3x + 1.
- f'(x) = 3x² - 3 = 3(x² - 1) = 3(x-1)(x+1)
- f'(x) = 0 when x = 1 and x = -1
Answer: Critical points at x = -1 and x = 1.
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Find the critical points of f(x) = x^(2/3).
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Practice
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