Chapter 13 - Partial Derivatives - 13.8 Maxima And Minima Of Functions Of Two Variables - Exercises Set 13.8 - Page 986: 23

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Let function $f(x, y)=x$ \[ 1=f_{x}(x, y)\quad \text { and } 0=\quad f_{y}(x, y) \] By theorem $13.8 .5,$ a point $\left(x_{0}, y_{0}\right)$ in the domain of a function $f(x, y)$ is called a critical point of the function if $f_{x}\left(x_{0}, y_{0}\right)=0$ and $f_{y}\left(x_{0}, y_{0}\right)=0$ or if one or both partial derivatives do not exist at $\left(x_{0}, y_{0}\right)$ So here $f_{x}(x, y)=1 \neq 0;$ there will be no critical point