What is a sample extrema problem?

1 Answer
David Y.
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+5yz=−x+5y, how do you find the maximum and minimum values for x+3y≤0, x−y≥0, 3x−7y≤16x+3y≤0,x−y≥0,3x−7y≤16?
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What is the maximum value that the graph of y=cosxy=cosx assumes?
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How do I find the maximum and minimum values of the function f(x)=x−2sin(x)f(x)=x−2sin(x) on the interval [−π4,π2]?
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How do you find the absolute maximum and minimum values of f on the given interval? f(x)=2x3−3x2−12x=1,[−2,3]
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