A) find y' if x^3 + y^3 = 6xy.
(b) find the tangent to the folium of descartes x3 + y3 = 6xy at the point (3, 3).
(c) at what point in the first quadrant is the tangent line horizontal?

Using derivative concepts, it is found that:

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Question a:

To solve this, we use the implicit differentiation. Thus:

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Question b:

This is at . So

Thus -1 is the answer.

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Question c:

Thus:

Thus:

The tangent line is horizontal at points , considering y > 0.

A similar problem is given at link