Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function f(x, y) at the critical point (x0, y0). fxx(x0, y0) = 25, fyy(x0, y0) = 9, fxy(x0, y0) = 13 saddle point relative maximum insufficient information relative minimum

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Asked Oct 20, 2019
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Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function f(x, y) at the critical point (x0, y0).
fxx(x0, y0) = 25, fyy(x0, y0) = 9, fxy(x0, y0) = 13
saddle point
relative maximum
insufficient information
relative minimum

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Expert Answer

Step 1

It is known that the second partials test for relative extrema is
d f(a,b)f(a,b)-[£s(0,b)]
1) If d >0 and f (a,b) >0 then f has relative minimum at (a,b
2) If d 0 and f(a,b) <0 then f has relative maximum at (a,b)
3) If d < lim 0 then (a,d,f(a,b)) is a saddle point.
4) Information when d 0
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It is known that the second partials test for relative extrema is d f(a,b)f(a,b)-[£s(0,b)] 1) If d >0 and f (a,b) >0 then f has relative minimum at (a,b 2) If d 0 and f(a,b) <0 then f has relative maximum at (a,b) 3) If d < lim 0 then (a,d,f(a,b)) is a saddle point. 4) Information when d 0

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Step 2

Obtain the value...

d f(X.). Y)-[ (x0, Yo)
25(9)-(13)
=225-169
-56
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d f(X.). Y)-[ (x0, Yo) 25(9)-(13) =225-169 -56

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