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Flip to reveal answersWhat are the steps of an optimisation problem?
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All 9 Flashcards — Optimisation
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Question
What are the steps of an optimisation problem?
Answer
Model the quantity → use the constraint to get one variable → differentiate → solve f'(x)=0 → classify → answer.
Question
Why must the quantity be in one variable?
Answer
You can only differentiate a function of a single variable.
Question
How do you eliminate the second variable?
Answer
Use the given constraint (fixed perimeter, total length, etc.) to substitute.
Question
How do you find the optimal value?
Answer
Solve f'(x) = 0.
Question
How do you confirm a maximum?
Answer
Show f''(x) < 0 (or that f' changes + to −) at that x.
Question
What form do many cost problems take?
Answer
A reciprocal model like T = ax + b/x.
Question
How do you differentiate b/x?
Answer
Write it as bx⁻¹; its derivative is −bx⁻² = −b/x².
Question
Why keep only positive solutions?
Answer
Lengths, volumes and similar physical quantities can't be negative.
Question
What should the final answer give?
Answer
Whatever the question asks — dimensions and/or the maximum/minimum value.
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Full study notes for Optimisation
Topic 5.8 hub
Optimisation & inflexion
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