Using First Derivative to Determine Monotonicity and Extrema
Let f(x) be differentiable on interval (a, b). 1. If f'(x) > 0 for all x in (a, b), then f(x) is monotonically increasing on (a, b). 2. If f'(x) < 0 for all x…
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CSCA Mathematics Formula Reference
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Let f(x) be differentiable on interval (a, b). 1. If f'(x) > 0 for all x in (a, b), then f(x) is monotonically increasing on (a, b). 2. If f'(x) < 0 for all x in (a, b), then f(x) is monotonically decreasing on (a, b). 3. If the sign of f'(x) changes around point x₀, then x₀ is an extremum point: positive to negative indicates a local maximum, negative to positive indicates a local minimum. If the sign does not change, x₀ is not an extremum point.
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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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