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# In given problem, find all critical points. Indicate whether each such point gives a local maximum or a local minimum, or whether it is a saddle point. Hint: Use Theorem C.$f(x, y)=x^2+4 y^2-2 x+8 y-1$

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Given $f\left(x,y \right)=x^{2}+4y^{2}-2x+8y-1$ Since $f_{x}\left( x,y\right)=2x-2$ and $f_{y}\left( x,y\right)=8y+8$ ,the critical point ,obtained by solving the simultaneous equations $f_{x}\left(x,y \right)=f_{y}\left(x,y \right)=0$ is $\left(1,-1 \right)$

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