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Astroids and Tangent Lines

The graph of x^(2/3) + y^(2/3) = 1 is an astroid.

How can I find the equation of the tangent line at (1/8, 3√3 /8). Are there any points on the curve at which no tangent line can be defined? Could you also explain?


Solution Summary

An astroid is investigated. The points on the curve a which no tangent is defined are found. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.