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The points where a function of two or more real variables attains its extremum values are found in the set containing the points where all first order partial derivatives vanish, the points where one or more of those derivatives does not exist, and the points where the function itself is discontinuous.
Example 1. The function
 from
 to
 has a (global) minimum point  , where its partial derivatives
 and
 both equal to zero.
Example 2. Also the function
 from
 to
 has a (global) minimum in  , where neither of its partial derivatives
 and
 exist.
Example 3. The function
 from
 to
 has an absolute minimum point
 , since
 ,
 , and
 for all
 .
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