Wolfram Function Repository
Instantuse addon functions for the Wolfram Language
Function Repository Resource:
Find the inflection points of a function of one variable
ResourceFunction["InflectionPoints"][expr, x] computes the inflection points of the expression expr with respect to variable x. 

ResourceFunction["InflectionPoints"][expr, x, "Classify"] computes the inflection points of the expression expr, along with the properties of these inflection points, with respect to variable x. 
Find the inflection points of a cubic function:
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Repeat the calculation, classifying the points of discontinuity:
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Find and classify the inflection points of another function:
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Find and classify the inflection points of a polynomial function:
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Find and classify the inflection points of a trigonometric function:
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Find and classify the inflection points of a generic functions using the "Domain" option:
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InflectionPoints will sometimes return results in terms of Root objects:
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Applying N to these outputs converts to an ordinary numeric result:
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For functions with a repeating pattern of inflection points, InflectionPoints returns results in terms of one or more undetermined constants, which can take any integer value:
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