Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Compute the regions on which an expression is monotonic
returns an association of information about where f is increasing, decreasing or constant with respect to x.
returns a specific property related to whether f is increasing, decreasing or constant with respect to x.
Compute the regions on which a curve is increasing, decreasing and constant:
Show plots as well as the regions:
FunctionMonotonicity returns strict regions of increasing and decreasing, as can be seen in this piecewise expression:
Return the "NumberLine" property to visualize the regions directly:
Or return the "Plot" property to visualize the regions on the plot of the curve:
Note that a curve can be both increasing and decreasing at a given point:
In this case, 0 is a member of both the increasing and decreasing regions. To test that this is true against the definition of a curve being strictly increasing for x≥0, use Resolve:
Likewise to test if the curve is decreasing for x≤0:
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