009A Sample Final 3, Problem 5

Calculate the equation of the tangent line to the curve defined by  $x^{3}+y^{3}=2xy$  at the point,  $(1,1).$

Foundations:
The equation of the tangent line to  $f(x)$  at the point  $(a,b)$  is
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=m(x-a)+b}   where  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m=f'(a).}

Solution:

Step 1:

Step 2:

Final Answer:

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