What the app does
f′ is differentiated again, and the sign of f″ is charted across the domain. Positive means concave up, holding water; negative means concave down. Where the sign changes and the function is defined, there is an inflection point.
Why it matters
Concavity is what separates two curves that rise at the same rate but bend opposite ways. It also settles ambiguous turning points: at a stationary point, f″ > 0 means a minimum and f″ < 0 a maximum.
Read further
- Second derivative Wikipedia
- Inflection point Wikipedia
- Concave function Wikipedia
- The shape of a graph, part II Paul's Online Notes