Stationary points are where the derivative is zero. They include peaks, troughs and saddle points.
Drag the point along the curve
y = x·x·x·x - 2·x·xat x = 1: slope ≈ 0
Three flavours of stationary point
- Local maximum — f′ changes + to −.
- Local minimum — f′ changes − to +.
- Stationary / horizontal inflection — f′ is zero but doesn't change sign (e.g. y = x³ at 0).
Your turn
Find the stationary points of f(x) = x⁴ − 2x² and classify them.
Watch out
'Stationary point' just means f′ = 0 — it does not automatically mean max or min. y = x³ has a stationary point at 0 that is neither.