An inflection point is a point on the curve where concavity changes. For the smooth functions here, solve \(f''(x)=0\), then confirm a change of sign. A discontinuity is not an inflection point.

Both stationary and non-stationary points of inflection are required in AA HL. In contrast, \(y=x^4\) is concave up on both sides of zero and has no inflection there.

Concavity of Graphs

Applications of Differentiation

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Concavity and Points of Inflection

Concavity and Points of Inflection