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\textbf{Applications of Partial Differentiation}

\textit{\textbf{Extremes}}
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\textbf{Question}

Find and classify the critical points of the function

$$f(x,y)=xy-x+y$$


\textbf{Answer}

\begin{eqnarray*}
f_1 &amp; = &amp; y-1\\
f_2 &amp; = &amp; x+1\\
A &amp; = &amp; f_{11} =0\\
B &amp; = &amp; f_{12} =1\\
C &amp; = &amp; f_{22} =0
\end{eqnarray*}
Critical point $(-1,1)$ is a saddle point since $B^2-AC&gt;0$.

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