Practical maxima and minima
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 4 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- The cheapest tin
- The plan
Read the transcript of the teaching part
Last time
Before we start: last time, in Stationary points and the derivative tests, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
The cheapest tin
A manufacturer wants a tin that holds a litre using the least metal. Too tall and thin wastes metal on the sides. Too short and wide wastes it on the ends. Somewhere in between is the cheapest shape, and calculus finds it exactly.
The plan
One: draw the shape and name the variables. Two: write the quantity to optimise, such as area or cost, in terms of two variables. Three: use the given condition to eliminate one variable. Four: differentiate, set it to zero, and solve. Five: prove it is a maximum or a minimum, and answer the question asked.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Practical maxima and minima.
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.