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I have posted a link there to this thread so the OP can view my work.Calculus- find the points on the astroid where the tangent line has slope 1?

The equation of the astroid is x^(2/3) + y^(2/3) =1

I found that the derivative is -(y/x)^(1/3) = y'

I'm not sure how to get the points where the tangent line has slope one though- I tried plugging in one for y'; I just got -x =y, which seems right considering the answers, but I'm not sure how to get specific points.

According to the book, the answers are (2^(1/2)/4, 2^(1/2)/-4) and (2^(1/2)/-4,2^(1/2)/4)

I'd appreciate any help in the right direction.