Mathematical Methods · second derivative · manipulative

Bowl, hill, or the test is silent

Stand on a stationary point. If f″ > 0 the curve is a bowl (local min). If f″ < 0 it is a hill (local max). If f″ = 0 the test cannot decide — look at x³ and x⁴.

y = f(x) f″ > 0 bowl f″ < 0 hill f″ = 0 silent

Use Jump to stand on each stationary point · scroll zoom · pan

Stationary point

Working