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math: add optimisation

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eggy 2020-11-20 19:51:31 -05:00
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@ -602,6 +602,17 @@ Changes in concavity only occur at points of inflection.
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.
### Optimisation
To optimise for a maximum or minimum of a variable:
- Identify an equation with only one variable dependent on another
- Find the first derivative and identify critical points
- Use the second derivative test to identify if the critical point is a maximum or minimum
- Check constraints and throw away any inadmissible results
Diagrams with labelled variables may be helpful.
## Resources
- [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)