Question

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

Answer 1

*f(x,y)

Answer 2

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

Answer 3

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

Answer 4

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.

Answer 5

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.

Answer 6

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

Answer 7

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.

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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.

Answer 15

Alright, thank you!

Answer 16

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)

Answer 17

I'm sorry min (not max)