Answer to Question #293139 in Calculus for Sowmhb

Question #293139

Given fxx=6x,fxy=0,fyy=6y, find the nature of stationary point at (-1,2)

1
Expert's answer
2022-02-03T09:01:46-0500

Solution:

fxx=A=6x,fxy=B=0,fyy=C=6yf_{xx}=A=6x, \\f_{xy}=B=0, \\f_{yy}=C=6y

At (-1,2),

A=6(1)=6B=0C=6(2)=12A=6(-1)=-6 \\B=0 \\C=6(2)=12

Now, we find ACB2AC-B^2

=(6)(12)02=72<0=(-6)(12)-0^2 \\=-72<0

So, nature of stationary point at (-1,2) is a saddle point, neither maximum nor minimum.


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