The maximum principle
Continuous functions whose domain is a closed enjoy two useful properties:
- the maximum principle
- the intermediate value theorem
This card covers the first. If a function is continuous and it's domain is a closed interval, then it has a maximum value (one or more values of the domain map to a maximum).
Bounded functions
Let
We say that
We say that
We say that
[...] are bounded
Let
Obtains maximum/minimum
Let
We say that
We say that
Maximum principle
Let
Then there is an
Similarly, there is an