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Plot ill Behaved Equation

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Thomas D. Dean

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Apr 5, 2013, 7:22:59 PM4/5/13
to
eq:=x^2*y(x)-y(x)^3=8;
I want to plot this in the vicinity of (-3,1);
subst({x=-3,y=1},eq);

How do I do this?

The slope of eq at (-3,1) is 1.

eq:=x^2*y(x)-y(x)^3=8;
eq1:=diff(eq,x);
eq2:=solve(eq1,diff(y(x),x));
de:=unapply(eq2,x,y);
de(-3,1);

However, if I use RealDomain and plot eq, the slope appears to be -1.

I want to get the equation of the tangent line at (-3,1) which is
y-1=x+3, if I use de(-3,1) for the slope.

I think the tangent line should be y-1=-(x+3) if the RealDomain plot is
correct.

Tom Dean
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