What is optimisation in calculus?
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What is optimisation in calculus?
Optimisation in calculus is the process of finding the maximum or minimum values of a function.
True or False?
Optimisation problems always involve multiple variables.
False.
Optimisation problems typically involve a quantity dependent on a single variable.
Sometimes a problem in multiple variables will need to be rewritten first in terms of a single variable.
What is the first step in solving an optimisation problem?
The first step in solving an optimisation problem is rewriting the quantity to be optimised in terms of a single variable, using any given constraints if necessary.
Why might finding stationary points be appropriate for a function used in an optimisation problem?
Finding stationary points for a function used in an optimisation problem can be important because stationary points include all local maximum and minimum points.
How can the second derivative be used in optimisation problems?
In optimisation problems, the second derivative can be used to determine the nature of stationary points (maximum or minimum).
True or False?
When the first part of an optimisation problem is a "show that" question, you may still be able to access later parts of the question even if you can't complete this initial step.
True.
When the first part of an optimisation problem is a "show that" question, you may still be able to access later parts of the question even if you can't complete this initial step.
For example a formula or equation may be included in the 'show that' part. That formula can be used in later parts, even if you don't answer the 'show that' part.
What is the final step in answering an optimisation question?
The final step in answering an optimisation question is interpreting the answer in the context of the question.