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- anonymous

When f(x,y_=x^3+y^2-6xy+9x+5y+2, find d(x,y) as used in the second derivative test.

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- anonymous

When f(x,y_=x^3+y^2-6xy+9x+5y+2, find d(x,y) as used in the second derivative test.

- schrodinger

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- anonymous

*f(x,y)

- 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

Your first step is to find derivative x and treat y as a constant

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- 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

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

There are no values for x and y stated in the question... hmm

- 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

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

Now I remember, critical points. You have to find critical points and input it.

- 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

I got x=2 and x=4 but I'm not sure if it has relevance to the question.

- anonymous

I got x=2 and x=4 but I'm not sure if it has relevance to the question.

- anonymous

Yeah, 2, 4 are x values now plug it in other eq and y values.

- 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

Alright, thank you!

- 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

I'm sorry min (not max)

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