(adsbygoogle = window.adsbygoogle || []).push({}); At what points on the curve (y-2)^3 + y(x-6) = 0 does dy/dx not exist?

So I've tried a few approaches:

1. find point where dx=0, since -Fx/Fy = dy/dx, therefore also Fy=0. So I took the partial derivative wrt y and got another equation, 3(y-2)^2 + (x-6) = 0. From here I dont know where to go.

2. Graphically:

[PLAIN]http://www4c.wolframalpha.com/Calculate/MSP/MSP296019ha1c8h91aed5c300005983bc124ea5gai3?MSPStoreType=image/gif&s=10&w=200&h=205&cdf=Coordinates&cdf=Tooltips [Broken]

From this it would seem that approximately when x<-20, there is no derivative or no defined derivative since there is more than one?

But how do I find this algebraically?

Thanks

Jay

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# Homework Help: Ordinary Differential Equation: At what points on the curve does the F'(x) not exist?

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