Optimization is simply finding the maximum or minimum possible value. In order to prove that a value is a maximum or minimum, one needs to prove that the value is attainable and that there is no higher or lower value (depending on the problem) that works.
- There are multiple ways to determine the maximum or minimum (depending of the leading term) of a quadratic (depending on the form).
- The maximum of and is 1, and the minimum of and is -1.
- We can use inequalities like AM-GM Inequality for some optimization problems.
- We can also use coordinate geometry to determine the maximum or minimum for some problems. Optimization is often done when two figures touch each other exactly once.
- In calculus, for a function , the local maximums and local minimums are part of the critical points of the function. The x-values of the critical points can be found by taking the derivative of and setting it to equal 0. In order to find the absolute maximum or minimum, one needs to also check the endpoints of an interval.