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poi

Syntax

poi(function, variable)

Description

Finds and classifies points of interest of function. Currently it looks for

Stationary Points
- Classified as either maximum, minimum or inflection point. If either of the former two appear in capital letters this indicates that the point is a global extremum. Otherwise it is local.
Axes Intercepts
- These are classified according to which axis is intercepted.
Asymptotes
- Only finds straight line asymptotes.
- Classified as either horizontal, vertical or oblique.
- Provides the equation of the asymptote.
Endpoints
- Classified as either "open circle" (not part of function) or "closed circle" (part of function)

If there is an infinite number of points of interest, poi will try to deal with them using parameters. If it can't find all points of interest in exact mode it will go into approximate mode to try to find them.

Warnings

Sometimes this function will miss points. This can happen because sometimes the built in solve function doesn't find all solutions. Vertical asymptotes are often missed.

This function is known to not work with some functions such as sec(x).

Parameters

function

The function to investigate.

variable

The variable in function.

Examples

n44 and n50 are integers.