University students' grasp of inflection points

Pessia Tsamir*, Regina Ovodenko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper describes university students' grasp of inflection points. The participants were asked what inflection points are, to mark inflection points on graphs, to judge the validity of related statements, and to find inflection points by investigating (1) a function, (2) the derivative, and (3) the graph of the derivative. We found four erroneous images of inflection points: (1) f ′ (x) = 0 as a necessary condition, (2) f ′ (x) ≠ 0 as a necessary condition, (3) f ″ (x) = 0 as a sufficient condition, and (4) the location of "a peak point, where the graph bends" as an inflection point. We use the lenses of Fischbein, Tall, and Vinner and Duval's frameworks to analyze students' errors that were rooted in mathematical and in real-life contexts.

Original languageEnglish
Pages (from-to)409-427
Number of pages19
JournalEducational Studies in Mathematics
Issue number3
StatePublished - Jul 2013


  • Concept image
  • Definition
  • Inflection point
  • Intuition
  • Representation


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