anonymous
  • anonymous
When f(x,y_=x^3+y^2-6xy+9x+5y+2, find d(x,y) as used in the second derivative test.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
*f(x,y)
anonymous
  • anonymous
OK, your question may not be understandable due to difficulties with typing math. I think what you want is f subxy. Partial dervivative respect to x, then partial y
anonymous
  • anonymous
Your first step is to find derivative x and treat y as a constant

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anonymous
  • anonymous
fxx(x,y)=6x and fyy(x,y)=2 and fxy(x,y)=-6, and I got D=6x(2)-(-6)^2=12x-36 which is the answer... but I don't know where I got 6x(2)-(-6)^2 from previously.
anonymous
  • anonymous
Your fxx, fyy, fxy is correct. In order to find D you need to in put given values of x and y where applicable. Look over the original question you should have values for x and y.
anonymous
  • anonymous
There are no values for x and y stated in the question... hmm
anonymous
  • anonymous
This is just a general question preparing you for test, like you said. He is just giving you practice and there was no mention of D; just instinctively attempted to find it. In a real to find D you need to input values. (I see you were absent-mindedly putting in 2 and -6 as your values.
anonymous
  • anonymous
Its a multiple choice question and I got it correct last week but can't seem to figure out why I used those values. Haha
anonymous
  • anonymous
Now I remember, critical points. You have to find critical points and input it.
anonymous
  • anonymous
Use f sub x and f sub y; set both to zero. Solving f sub y: x=(2y+5)/6 Plug this x value in f sub x
anonymous
  • anonymous
I got x=2 and x=4 but I'm not sure if it has relevance to the question.
anonymous
  • anonymous
I got x=2 and x=4 but I'm not sure if it has relevance to the question.
anonymous
  • anonymous
Yeah, 2, 4 are x values now plug it in other eq and y values.
anonymous
  • anonymous
Ok when you plug them in critical values are (2, 7/2) and (4, 19/2). These are critical points potential relative min, max at these points. These are points you work with separately to find D.
anonymous
  • anonymous
Alright, thank you!
anonymous
  • anonymous
Perhaps this going beyond a multiple choice question: in both cases D is greater than zero, f sub xx is greater than zero therefore local or relative max at (2, 7/2) and (4,19/2)
anonymous
  • anonymous
I'm sorry min (not max)

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