Turn a word problem into one equation, differentiate it to find the maximum or minimum, and interpret rates of change in real units.
By the end, you can
set up an optimisation problem, solve it with calculus and interpret a rate of change correctly.
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Optimisation and Rates of Change
Calculus applied to a real question
What box shape uses the least cardboard? At what price does profit peak? How fast is the water level dropping? 📦
These are optimisation questions, and the calculus in them is easy. The difficulty is always the setup — turning the words into one equation with one variable.
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Optimisation and Rates of Change
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Next on the Mathematics P1 path · step 9 of 11
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Solve linear and non-linear systems by substitution, keep your ordered pairs matched, and handle the exponent-law questions that look harder than they are.
Read a hyperbola from its equation — both asymptotes, the shape, the axes of symmetry and its domain and range — and sketch it with confidence.
Work through quadratics, the formula, surd equations and inequalities with a method you can trust under pressure, and learn where marks are usually lost.
Tell arithmetic patterns from quadratic ones using differences, build the general term for each, and read sigma notation without panic.
Use the first and second derivatives to analyse a cubic graph, locate turning and inflection points, and build the equation of a tangent.
The whole Mathematics P1 path → All High School MicroQuests → Browse all 134 →
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Optimisation and Rates of Change
R19 · 14 min · certificate
