Level curve (source code)

= Level curve
{title2=$f(x,y)=c$}

A <level curve> is the planar <level set> of a scalar function. Where the gradient does not vanish, the <implicit function theorem> makes it locally a smooth curve. At a <critical point>, branches may cross, narrow into a cusp or shrink to a point, so a plot should be interpreted with the local critical-point analysis.