Necessary Condition for Local Extrema Using Derivative (Fermat's Lemma)
Let function f(x) be differentiable at point x₀. If f(x) attains a local extremum (maximum or minimum) at x₀, then it must be that f'(x₀) = 0. A point x₀ satis…
Syllabus path: Functions › Concepts and Properties of Functions › Maximum and Minimum Values of a Function
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CSCA Mathematics Formula Reference
Formula and explanation
Let function f(x) be differentiable at point x₀. If f(x) attains a local extremum (maximum or minimum) at x₀, then it must be that f'(x₀) = 0. A point x₀ satisfying f'(x₀) = 0 is called a stationary point (or critical point) of f(x).
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Maximum and Minimum Values of a Function
Maximum and Minimum Values of a Function 1. Concept The Maximum and Minimum Values (collectively called Global Extrema) describe the boundaries of the function's output range over its entire domain or a specific interval. Let the domain of y = f(x) be D: Maximum Value: If there e…
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