math: add optimisation
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@ -602,6 +602,17 @@ Changes in concavity only occur at points of inflection.
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A cusp is a point on a continuous function that is not differentiable as the slopes on both sides approach -∞ and ∞. Concavity does not change at a cusp, but they may be considered for local extrema.
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A cusp is a point on a continuous function that is not differentiable as the slopes on both sides approach -∞ and ∞. Concavity does not change at a cusp, but they may be considered for local extrema.
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### Optimisation
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To optimise for a maximum or minimum of a variable:
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- Identify an equation with only one variable dependent on another
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- Find the first derivative and identify critical points
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- Use the second derivative test to identify if the critical point is a maximum or minimum
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- Check constraints and throw away any inadmissible results
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Diagrams with labelled variables may be helpful.
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## Resources
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## Resources
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- [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)
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- [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)
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