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RE: Plotting an implicit function


Use r_ and M_ in the definition, and I prefer a definition as a function and
not an equation so we can test evaluate or Plot the function for various

f[r_, M_] := 1 + (-1 - 0.03*M^2 + 1.2*M)*r -
   ((0.05*E^(r*M))/r - 0.05/r + E^(r*M)*(1 - 0.05*M))

The following seems to give the plot that you are looking for. I fixed the
aspect ratio to get a better representation and also extended the M domain
to obtain a better picture of the function.


ImplicitPlot[f[r, M] == 0, {M, 0, 30}, {r, 0.0001, 0.03},
    AspectRatio -> 1,
    Frame -> True,
    FrameLabel -> {M, r}];

David Park
djmp at

From: David Friskin [mailto:david.friskin at]
To: mathgroup at

I have the following implicit function:
f[r, M]=1 + (-1 - 0.03*M^2 +
    1.2*M)*r - (0.05*E^(r*M)/r - 0.05/r + E^(r*M)*(1 - 0.05*M))==0

where r is a function of M i.e. r(M).

I would like to plot r(M) vs M, for {M,0,20}.

I tried using
 ImplicitPlot[{f[r,M] == 0},{M,0,20}], but Solve is having problems
finding the roots to my function.

Could someone help me with the code to do this, perhaps using FindRoot


P.S. r > 0

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