Steps to Find Extrema of a Continuous Function on a Closed Interval
To find the maximum and minimum values of a function f(x) on the closed interval [a, b]: 1. Find all critical points (where f'(x) = 0 ) and points where the de…
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
To find the maximum and minimum values of a function f(x) on the closed interval [a, b]: 1. Find all critical points (where f'(x) = 0 ) and points where the derivative does not exist within the open interval (a, b). 2. Compute the function values at these points and at the endpoints a and b. 3. Compare these function values. The largest is the maximum, and the smallest is the minimum. Applicable Condition: The function is continuous on [a, b] and differentiable on (a, b) (or has only a finite number of points where it is not differentiable).
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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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