007A Sample Final 1, Problem 8

A curve is defined implicitly by the equation

$x^{3}+y^{3}=6xy.$

(a) Using implicit differentiation, compute  ${\frac {dy}{dx}}$.

(b) Find an equation of the tangent line to the curve  $x^{3}+y^{3}=6xy$  at the point  $(3,3)$.

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Solution

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