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Question: Implicit differentiation (finding extreme values)

Question:Implicit differentiation (finding extreme values)

Lizard King 12 Maple
plot
December 02 2007
0
Hello, I have a problem with this implicit equation: > eq:=(x^2+4*y)^2+(x+y^2)^2=65 I can find the tangent line for a point on the curve, e.g. (-2,1). This is the slope on the point. > a:=subs(y=1,x=-2,implicitdiff(eq,y,x)); It will give this tangent line. > tanline:=a*(x+2)+1; Here's a plot: Image and video hosting by TinyPic But now I want to find the locations of its extreme values. That's where I got stuck. The tangent line must be horizontal so dy/dx = 0. So I have to the implicit equation for the condition dy/dx=0. For explicit functions it's not that hard, e.g.: > y:=x^2*sin(x); > p:=fsolve(diff(y,x)=0,x=1..3); > locmax:=eval(y,x=p); But in mine case this doesn't work > solve(implicitdiff(eq,y,x)=0,y,x); Says invalid arguments. How do I get this working? Any ideas?
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