Using the Second Derivative to Determine Extrema
Suppose function f(x) has a second derivative at point x₀, and f'(x₀) = 0, f''(x₀) e 0, then: - If f''(x₀) < 0, f(x) attains a local maximum at x₀. - If f''(x₀…
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CSCA Mathematics Formula Reference
Formula and explanation
Suppose function f(x) has a second derivative at point x₀, and f'(x₀) = 0, f''(x₀) e 0, then: - If f''(x₀) < 0, f(x) attains a local maximum at x₀. - If f''(x₀) > 0, f(x) attains a local minimum at x₀. If f''(x₀) = 0, this test is inconclusive, and other methods (like the first derivative test) must be used. Applicable Condition: The function is twice differentiable at x₀, and its first derivative is zero.
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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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