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Let f be a function with two variables with continuous second order partial derivatives fxx, fyy and fxy at a critical point (a,b). Let
D = fxx(a,b) fyy(a,b) - fxy2(a,b)
If D > 0 and fxx(a,b) > 0, then f has a relative minimum at (a,b).
If D > 0 and fxx(a,b) < 0, then f has a relative maximum at (a,b).
If D < 0, then f has a saddle point at (a,b).
If D = 0, then no conclusion can be drawn.
We now present several examples with detailed solutions on how to locate
relative minima, maxima and saddle points of functions of two
variables. When too many critical points are found, the use of a table
is very convenient.
y=9 or 2
minima= (5, 2)
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