finds the monotonicity of the function f with the variable x over the reals.
finds the monotonicity of f when x is restricted to the domain dom.
gives the monotonicity of f when x is restricted by the constraints cons.
Details and Options
- Monotonicity is also known as increasing, decreasing, non-decreasing, non-increasing, strictly increasing and strictly decreasing.
- By default, the following definitions are used:
+1 non-decreasing, i.e. for all 0 constant, i.e. for all -1 non-increasing, i.e. for all Indeterminate neither non-decreasing nor non-increasing
- The constant function is both non-decreasing and non-increasing.
- With the setting StrictInequalitiesTrue, the following definitions are used:
+1 increasing, i.e. for all -1 decreasing, i.e. for all Indeterminate neither increasing nor decreasing
- Possible values for dom include: Reals, Integers, PositiveReals, PositiveIntegers, etc. The default is Reals.
- The function f should be a real-valued function for all x in the domain dom that satisfy the constraints cons.
- cons can contain equations, inequalities or logical combinations of these.
- The following options can be given:
Assumptions $Assumptions assumptions on parameters GenerateConditions True whether to generate conditions on parameters PerformanceGoal $PerformanceGoal whether to prioritize speed or quality StrictInequalities True whether to require strict monotonicity
- Possible settings for GenerateConditions include:
Automatic non-generic conditions only True all conditions False no conditions None return unevaluated if conditions are needed
- Possible settings for PerformanceGoal are "Speed" and "Quality".
Examplesopen allclose all
Basic Examples (3)
A function that is not real valued has Indeterminate monotonicity:
FunctionMonotonicity gives a conditional answer here:
By default, FunctionMonotonicity may generate conditions on symbolic parameters:
Use PerformanceGoal to avoid potentially expensive computations:
Basic Applications (6)
For comparison, compute the range using FunctionRange:
Use Sum to compute the sum of the series:
Equation Solving and Optimization (2)
Use Solve to find the root:
Properties & Relations (2)
Wolfram Research (2020), FunctionMonotonicity, Wolfram Language function, https://reference.wolfram.com/language/ref/FunctionMonotonicity.html.
Wolfram Language. 2020. "FunctionMonotonicity." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FunctionMonotonicity.html.
Wolfram Language. (2020). FunctionMonotonicity. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FunctionMonotonicity.html