#### michael.wes

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This topic has been masterfully avoided in my classes, but several proofs of theorems in multivariate calculus use the existence of a parametrization like this:

Let [tex]f:\mathbb{R}^2\to\mathbb{R}[/tex]. Then we can write: [tex]f(x,y)=g(t)=f(x(t),y(t))[/tex]

And from this, we can get some interesting results, like the Lagrange multiplier theorem. However, an existence proof has eluded me online and my professor's explanation was essentially that whenever the level curves of f are smooth, closed curves, this parametrization "can be done". Can anyone help me with this, or direct me to a source (maybe even on these forums) that has the proof?

Thanks