critical points
Where derivatives vanish
Critical points are locations or moments where something significant changes or could go either way.
In mathematics, a critical point is where a function's derivative equals zero or is undefined—these are the spots where curves peak, bottom out, or flatten.
In physics and chemistry, a critical point marks specific conditions (temperature and pressure) where distinct phases of matter become indistinguishable.
More broadly, critical points refer to decisive junctures: We've reached a critical point in the negotiations.
- bifurcationDivision into two branches
- extremaFunction's highest, lowest points
- phase transitionMatter shifting between states
- maximaGreatest possible values
- junctureCritical point of decision
crossroads · minima · make or break · Lyapunov exponents · optimization · equilibrium · threshold · singularities · stationary · derivative · vertex · differential equations · peak · gradient · tangent · zero · curve · saddle
- calculusderivatives, integral, integrals, limits, differential calculus
- dynamical systemsattractors, attractor, chaos theory, equilibria, bifurcation
- scalingscalability, power laws, horizontal scaling, self-similarity, proportionality
- statistical mechanicsentropy, thermal equilibrium, phase transition, fluctuations, free energy
critical pointsminor points
Insignificant matters for debate
background noise · irrelevancies · afterthoughts · fine print
critical pointsground state
Lowest possible energy configuration
crisis, critical, points, pointer, critique, point, uncritical, hypercritical, overcritical