Stationary points and the derivative tests
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 2 worked examples, 4 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- The top of the hill
- Stationary points
Read the transcript of the teaching part
Last time
Before we start: last time, in Tangents and normals, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
The top of the hill
At the top of a hill, you stop going up and have not yet started going down. For a moment, the slope is zero. Those points on a graph, where the gradient is zero, are stationary points. Finding them, and deciding whether each is a top or a bottom, is one of the most tested skills in the paper.
Stationary points
A stationary point is where dy by dx equals zero. The tangent is horizontal. It can be a maximum, a minimum, or a point of inflection where the curve flattens as it passes through. To find them: differentiate, set it equal to zero, solve for x, then find y for each.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Stationary points.
The whole chapter: Applications of Differentiation.
Chapter 14: Differentiation and integration
- Differentiation: standard functions, chain, product and quotient rules 5 min
- Tangents and normals 5 min
- Stationary points and the derivative tests 5 min
- Practical maxima and minima 5 min
- Connected rates of change and small increments 5 min
- Integration: powers of x and the reverse of differentiation 5 min
- Integrating (ax + b)ⁿ, exponentials and trigonometric functions 5 min
- Definite integrals and plane areas 5 min
- Kinematics: displacement, velocity, acceleration and graphs 5 min
Also for O Level Additional Maths 4037
Which topics come up most in O Level Additional Maths 4037 past papers, counted from every paper since 2004.