KnowraSecond derivative testLinked fromLinked fromThe 8 pages that link to Second derivative test, each with the reason it gives.All 8Broader topic 1Related 7Hessian matrixRelated: The multivariable test examines Hessian definiteness at a critical point.Convex functionRelated: For twice-differentiable functions on an interval, nonnegative second derivative characterizes convexity.Maximum and minimumRelated: Positive curvature indicates a local minimum and negative curvature a local maximum under the test's conditions.Second derivativeBroader topic: At a stationary point, its sign can distinguish a local maximum from a local minimum.Sylvester's criterionRelated: Its multivariable form often reduces to testing the Hessian with this criterion.Interior extremum theoremRelated: It adds information the first-order necessary condition cannot provide.Principle of minimum energyRelated: Positive curvature of energy in allowed directions indicates a local minimum.Symmetry of second derivativesRelated: The symmetric Hessian supplies the curvature information used in the test.