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Answer by eldo for Finding maximum or minimum of implicit functions
f = x^2 + y^2 - (2 x^2 + 2 y^2 - x)^2;points = Catenate[{x, y} /. MapThread[Solve[{f == 0, -D[f, #1]/D[f, #2] == 0}, {x, y}, Reals] &, {{x, y}, {y, x}}]]grid = Union /@...
View ArticleAnswer by chyanog for Finding maximum or minimum of implicit functions
Reduce[x^2+y^2==(2 x^2+2 y^2-x)^2,{y},{x},Reals]-((3 Sqrt[3])/8) <= y <= (3 Sqrt[3])/8
View ArticleAnswer by Szabolcs for Finding maximum or minimum of implicit functions
In version 10,RegionBounds@ImplicitRegion[x^2 + y^2 == (2 x^2 + 2 y^2 - x)^2, {x, y}](* {{-(1/8), 1}, {-((3 Sqrt[3])/8), (3 Sqrt[3])/8}} *)
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Answer by eldo for Finding maximum or minimum of implicit functions
Also just for fun (in case you don't like to solve equations):cp = ContourPlot[x^2 + y^2 == (2 x^2 + 2 y^2 - x)^2, {x, -1, 2}, {y, -1, 1}, AspectRatio -> Automatic];x = Cases[cp, {_Real, _Real},...
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Answer by ubpdqn for Finding maximum or minimum of implicit functions
I post this just for fun. It does not address the general question of maximizing implicit function but Kuba has shown how to maximize y subject to constraint f(x,y).The problem can (with a small amount...
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Answer by Bob Hanlon for Finding maximum or minimum of implicit functions
This implicit equation is simple enough to be converted to explicit equationseqn = x^2 + y^2 == (2 x^2 + 2 y^2 - x)^2;yExpr = (y /. Solve[eqn, y]);yMax = SortBy[Maximize[#, x] & /@ yExpr,...
View ArticleAnswer by Kuba for Finding maximum or minimum of implicit functions
Maximize[{y, x^2 + y^2 == (2 x^2 + 2 y^2 - x)^2}, {x, y}]{(3 Sqrt[3])/8, {x -> 3/8, y -> (3 Sqrt[3])/8}}
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Answer by Mark McClure for Finding maximum or minimum of implicit functions
You could use Lagrange multipliers to maximize $f(x,y)=y$ subject to the constraint that$$g(x,y) = x^2 + y^2 - (2 x^2 + 2 y^2 - x)^2 = 0.$$f[x_, y_] = y;g[x_, y_] = x^2 + y^2 - (2 x^2 + 2 y^2 -...
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Answer by molekyla777 for Finding maximum or minimum of implicit functions
You function isf = x^2 + y^2 - (2 x^2 + 2 y^2 - x)^2;Then call function MaximizeMaximize[f, {x, y}](*{27/64,{x->3/4,y->0}}*)And here is plot of you function
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Finding maximum or minimum of implicit functions
is there any built in function that can be used to find maximum or minimum of implicit functions?For example, if we have the equation$$x^2 + y^2 = (2 x^2 + 2 y^2 - x)^2,$$then we can visualize the set...
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