AP Calculus AB : How to graph functions of points of inflection

Study concepts, example questions & explanations for AP Calculus AB

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Example Questions

Example Question #1 : How To Graph Functions Of Points Of Inflection

Which of the following functions has exactly one point of inflection?

Possible Answers:






Correct answer:



For any function, a point of inflection occurs when .  For a function to have exactly one point of inflection, it has to be of third order (i.e. have an  term as its highest order term).  The function  only has one point of inflection when .  

A linear equation does not have any points of inflection, nor does a quadratic equation or exponential function.  

A function with an order higher than three has multiple points of inflection.

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