anonymous
  • anonymous
Extrema of Functions of two variables: Find the critical points of the function and from the form of the function determine whether a relative maximum or relative minimum occurs at each point. f(x,y,z)=9-(x(y-1)(z+2))^2
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Question since there are three terms instead of two does d become the following: \[d=f _{xx(a,b)f _{yy}}(a,b)f _{zz}(a,b)-f _{xy}(x,y)^2\] ^ this is the formula to test for relative extrema
anonymous
  • anonymous
Is this right: \[f _{x}(x,y,z)=-2x(y-1)^2(z+2))^2=0\] \[f _{y}(x,y,z)=-2x^2(y-1)(z+2))^2=0\] \[f _{x}(x,y,z)=-2x^2(y-1)^2(z+2))=0\] I get critical points of (0,1,-2)
anonymous
  • anonymous
The second derivatives are: \[f _{xx}(x,y,z)=-2(y-1)^2(z+2))^2\] \[f _{yy}(x,y,z)=-2x^2(1)(z+2))^2\] \[f _{zz}(x,y,z)=-2x^2(y-1)^2(1))\]

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anonymous
  • anonymous
So plugging the critical points into the problem d above (considering i'm using the right equation and its not the test for extrema of three variables) then my d is 0 which makes the problem inconcusive. Is this right?

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