# What is a sample extrema problem?

Feb 4, 2015

Extrema are the maximum and minimum values for a given range, and can be described as relative (pertaining to a local neighborhood) or absolute (pertaining to the whole set of possible values).

Some example problems for you to practice are:

Given the constraint z=−x+5y, how do you find the maximum and minimum values for x+3y≤0, x−y≥0, 3x−7y≤16?
What is the maximum value that the graph of $y = \cos x$ assumes?
How do I find the maximum and minimum values of the function f(x)=x−2sin(x) on the interval [−π4,π2]?
How do you find the absolute maximum and minimum values of f on the given interval? f(x)=2x3−3x2−12x=1,[−2,3]