Using Derivative to Determine Monotonicity of a Function
Let function f(x) be differentiable on the interval (a, b). - If f'(x) > 0 for all x in (a, b), then f(x) is monotonically increasing on (a, b). - If f'(x) < 0…
Syllabus path: Functions › Concepts and Properties of Functions › Monotonicity of Functions
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CSCA Mathematics Formula Reference
Formula and explanation
Let function f(x) be differentiable on the interval (a, b). - If f'(x) > 0 for all x in (a, b), then f(x) is monotonically increasing on (a, b). - If f'(x) < 0 for all x in (a, b), then f(x) is monotonically decreasing on (a, b). - If f'(x) = 0 for all x in (a, b), then f(x) is constant on (a, b). Note: This theorem applies to open intervals. For closed intervals, we usually consider the interior.
Related tutorial and examples
Monotonicity of Functions
Monotonicity of Functions 1. Concept Monotonicity describes the trend of a function's value as the independent variable increases. It is the mathematical expression for whether a graph is "rising" or "falling". Let the domain of function f(x) be D, and let I ⊆ D be an interval. M…
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