Use the Second Derivative Test to classify the critical points of f(x, y) = x^2 + 2y^2 - 4x + 4y + 6.

Ayaana Buck 2021-02-02 Answered
Use the Second Derivative Test to classify the critical points of f(x,y)=x2+2y24x+4y+6.
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tafzijdeq
Answered 2021-02-03 Author has 92 answers

To find the critical points : fx=0 and fy=0
fx=02x4=0x=2
and fy=04y+4=0y=1
Analyzing the second derivative test using the critical point: (x,y)=(2, -1) Let
A=fxx,B=fxy, and C=fyy
A=fxx=2,B=fxy=0, and C=fyy=4
ACB2=80=8>0
Therefore, at the point (2, -1) f is local maximum.

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Jeffrey Jordon
Answered 2021-11-07 Author has 2064 answers

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