Extreme Value Theorem for Continuous Functions on a Closed Interval
If a function f(x) is continuous on the closed interval [a, b], then f(x) must attain both a maximum and a minimum value on [a, b]. That is, there exist x₁, x₂…
Syllabus path: Functions › Concepts and Properties of Functions › Maximum and Minimum Values of a Function
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CSCA Mathematics Concept & Principle Guide
Concept, principle, and explanation
If a function f(x) is continuous on the closed interval [a, b], then f(x) must attain both a maximum and a minimum value on [a, b]. That is, there exist x₁, x₂ ∈ [a, b] such that for all x ∈ [a, b], f(x₁) ≤ f(x) ≤ f(x₂).
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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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