# Can a point of inflection be undefined?

See the explanation section below.

A point of inflection is a point on the graph at which the concavity of the graph changes.

Example

graph{1/x [-10.6, 11.9, -5.985, 5.265]}

Example 2

graph{x^(1/3) [-3.735, 5.034, -2.55, 1.835]}

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No, a point of inflection cannot be undefined. A point of inflection occurs where the concavity of a curve changes, meaning the second derivative of the function changes sign. However, it's possible for a function to have no points of inflection if its second derivative does not change sign anywhere in its domain.

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