Pure · Differentiation
Chapter 1 · 4
The idea
Stationary points (maxima and minima)
Where a curve is momentarily flat — found by setting dy/dx = 0 — and how the second derivative tells a maximum from a minimum, plus reading off where a curve is increasing or decreasing.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Pure · Differentiation
Stationary points (maxima and minima)
Where a curve is momentarily flat — found by setting dy/dx = 0 — and how the second derivative tells a maximum from a minimum, plus reading off where a curve is increasing or decreasing.
Why it works
Flat for an instant
A stationary point is a spot where the curve is, for an instant, perfectly flat — its gradient is zero. Since the gradient is , finding stationary points is a single step: set and solve. (Not — that finds where the curve crosses the -axis, a completely different thing.)Full coordinates
That usually gives more than one answer — a cubic's gradient is a quadratic, so expect up to two stationary points — and each needs its put back in (using the original equation, not the derivative) to give full coordinates. Half a coordinate is half the marks.Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
Start freeTakes a minute — no card.