How do we find the critical point using partial derivatives?
By Joseph Russell •
If $\frac{\partial f}{\partial x}= 0$ when $x = 1$, and $\frac{\partial f}{\partial x} = (2y-x)$
Do we have to replace $x$ by 1? to get the critical coordinate $y$?
$\endgroup$ 11 Answer
$\begingroup$The critical points occur when $f_{x}=f_{y}=0$. So, necessarily, any critical point must occur when $x=1$ so that we obtain $2y-1=0$ and $y=\frac{1}{2}$ as desired. So you are correct.
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