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Find the critical points when $f(x,y) = x^2 + y^2 + 1$

This is just a simplified version of a much harder question I am doing.

I am hung up on the equation as I do not know to find the critical point since $f'(x,y)$ for $x$ is just $2x$.

In what way am I meant to follow this up to get the critical point. Any advice/help would be much appreciated. Thank you.

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Hint: A critical point occurs at some point $(a, b)$ when $\nabla f(a, b) = (0, 0)$. Hence in this case you have that \begin{align} \nabla f(a, b) = (2a, 2b) = (0, 0) \ \ \Rightarrow \ \ (a, b) = (0, 0). \end{align}

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Or in polar coordinates you are minimizing $$ f(r,\theta)= r^2 +1 $$ which obviously is minimized when $r=0$.

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