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\noindent {\bf Problem statement} To the right is part of the graph of
$5x^3y -3xy^2 +y^3=6$.  Verify that $(1,2)$ is a point on this
curve. There's a nearby point on the curve whose coordinates are
$(1.07,u)$. What is an approximate value for $u$? There's a nearby
point on the curve whose coordinates are $(.98,v)$. What is an
approximate value for $v$?  There's a nearby point on the curve whose
coordinates are $(w,2.04)$. What is an approximate value for $w$?
Is the graph consistent with your answers?

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\noindent {\bf Hint} Compute a derivative and use linear approximation.

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