Detachment and Tendency of a Single Variable Function
Detachment and Tendency of a Single Variable Function
Depicted are the pointwise operators: "detachment from left or right" and "tendency" applied to a given function. In the suggested graphs, the value of the one-sided detachments is colored in green, and the value of the tendency is colored in red.
The definition of the detachment is intuitive: the detachment from the left or right is the limit (from the left or right) of the sign of . The definition of the tendency is based on the one-sided detachments: if they are equal, then the tendency is 0; otherwise, the tendency equals the right detachment. Thus, a function's tendency in many cases simulates the sign of the derivative—without calculating the derivative first (this calculation saving has advantages in theory and applications).
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