Using Second Derivative to Determine Extrema (Sufficient Condition)
Let f(x) have a second derivative at point x₀, with f'(x₀) = 0 and f''(x₀) e 0. 1. If f''(x₀) > 0, then f(x) attains a local minimum at x₀. 2. If f''(x₀) < 0,…
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CSCA Mathematics Formula Reference
Formula and explanation
Let f(x) have a second derivative at point x₀, with f'(x₀) = 0 and f''(x₀) e 0. 1. If f''(x₀) > 0, then f(x) attains a local minimum at x₀. 2. If f''(x₀) < 0, then f(x) attains a local maximum at x₀. If f''(x₀) = 0, this method fails, and other methods (e.g., first derivative sign test) must be used.
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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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