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

Use the Second Derivative Test to classify the critical points of $f\left(x,y\right)={x}^{2}+2{y}^{2}-4x+4y+6.$
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To find the critical points : ${f}_{x}=0$ and ${f}_{y}=0$
${f}_{x}=0⇒2x-4=0⇒x=2$
and ${f}_{y}=0⇒4y+4=0⇒y=-1$
Analyzing the second derivative test using the critical point: (x,y)=(2, -1) Let
$A={f}_{xx},B={f}_{xy},$ and $C={f}_{yy}$
$A={f}_{xx}=2,B={f}_{xy}=0,$ and $C={f}_{yy}=4$
$AC-{B}^{2}=8-0=8>0$
Therefore, at the point (2, -1) f is local maximum.

Jeffrey Jordon