What is a sample extrema problem?

1 Answer
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#?
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What is the maximum value that the graph of #y=cosx# assumes?
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How do I find the maximum and minimum values of the function #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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