If a univariate real function has a single critical point
and that point is a local maximum, then has its global maximum
there (Wagon 1991, p. 87). The test breaks downs for bivariate functions, but
does hold for bivariate polynomials of degree . Such exceptions include
(1)
(2)
(3)
(Rosenholtz and Smylie 1985, Wagon 1991). Note that equation (3) has discontinuous partial derivatives
and ,
and
and .
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A
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in Action. New York: W. H. Freeman, pp. 87-91 and 228, 1991.
has a single critical point
and that point is a local maximum, then 
has its global maximum
there (Wagon 1991, p. 87). The test breaks downs for bivariate functions, but
does hold for bivariate polynomials of degree 
. Such exceptions include
and 
,
and 
and 
.
