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EAMCET Engineering 2004 Solved Paper

Section: Mathematics

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Question : 151 of 160

Marks: +1, -0

f(x, y)=2(x-y)^2-x^4-y^4

\left| (f_{xx} f_{yy} - f_{xy}^2) \right|_{(0,0)}

32
16
0
-1

Solution:

Given that,

f(x, y)=2(x-y)^2-x^4-y^4 \text{, we get }

On differentiating partially w.r.t.

x

,

f_x=4(x-y)-4x^3

Again differentiating partially, we get

f_{xx}=4-12x^2

\Rightarrow (f_{xx})_{(0,0)}=4-0=4

\& =4-12y^2

\text{ Similarly } f_{yy}=4-4

\Rightarrow (f_{yy})_{(0,0)}=4-0=4

\text{ and } f_{xy}=-4+0

\Rightarrow (f_{xy})_{(0,0)}=-4

\therefore (f_{xx} f_{yy} - f_{xy}^2)_{(0,0)} = 4(4)-(-4)^2=0

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