anonymous
  • anonymous
Find the local maximum and minimum values and saddle point(s) of the function. f(x, y) = x3y + 12x2 - 8y
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
i got fx(x,y)= 3x^2y+24 fy(xy)= x^3-8
anonymous
  • anonymous
fxx (x,y) = 6xy+ 24 fyy(x,y)= 3x^2 so x=0,-8, 2
anonymous
  • anonymous
What do you mean x=0, -8, 2? What is that the result of?

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anonymous
  • anonymous
setting the fx and fy =0
anonymous
  • anonymous
i am not sure of what i am suppose to do really past finding the partial derv.
myininaya
  • myininaya
fx=3x^2y+24x (this was the only mistake i seen from above so far) fy=x^3-8 fxx=6xy+24 fyy=3x^2
myininaya
  • myininaya
i think you meant that since you did fxx right though
anonymous
  • anonymous
From fx and fy, you should set each to 0 and solve as simultaneous equations and you get (x,y) critical points.
anonymous
  • anonymous
is fxy= 3x^2?
myininaya
  • myininaya
yes
anonymous
  • anonymous
that is where i got the values for x. those are the critical points, right?
anonymous
  • anonymous
Critical points are from fx and fy. Set each to 0; solve as simultaneous equations for (x,y) critical points.
anonymous
  • anonymous
x=0,-8,2
myininaya
  • myininaya
fx=0 implies 3x^2y+24x=0 3x(xy+8)=0 3x=0 => x=0 xy+8=0 => x=-8/y fy=0 implies x^3-8=0 when x=2 x=2 => 2=-8/y =>y=-4
anonymous
  • anonymous
Evaluate fxx at critical points Evaluate fxy at critical points Evaluate fyy at critical points
anonymous
  • anonymous
Let's call above evaluations A (fxx) B (fxy) C (fyy)
myininaya
  • myininaya
it looks that the only only critical number is (2,-4)
myininaya
  • myininaya
point*
anonymous
  • anonymous
If AC-(B)^2>0 and A>0 local min If AC-B^2>0 and A<0 local max If AC-B^2<0 saddle point
anonymous
  • anonymous
let me work at this
anonymous
  • anonymous
its the saddle point
anonymous
  • anonymous
Good work

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