# Plotting results from Findroot

I know this has been asked, but I cannot seem to understand the solutions. What I need to know, because I have my first domiciliary test this Monday, is how to plot the output from FindRoot for a system of equations as the parameters vary

I havent even been able to do it with one equation either

Say I have define

g[x_, y_] := 2 x + y


I can define the function

t[y_] := FindRoot[g[x, y], {x, 1}]


Wich does give me an answer for different y, but when I plot

Plot[t[x], {x, 0, 1}]


It wont do anything. I mean, the axis appear but nothing will be drawn on it.

If I had a system of equations, FindRoot would give several values, say {x, y}.

How can I draw x[d], y[d], where this last two are the roots of FindRoots for different values of parameter d?

Thank you very much and I am very sorry if this is really simple but I havent been able to solve it.

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• You can format inline code and code blocks by selecting the code and clicking the {} button above the edit window. The edit window help button ? is also useful for learning how to format your questions and answers. – Michael E2 Jul 15 '15 at 1:38
• Have you look at the many other questions about plotting and FindRoot? You may find some help there. – Michael E2 Jul 15 '15 at 1:39
• I did. I try with several, specially making changes to this one, but in the solution i can not understand what [[1,2]] are, but i fI remove then it does not plot and it gives errors mathematica.stackexchange.com/questions/23573/… – Marco Eugenio Escobar Jul 15 '15 at 1:41
• Many of the answers suggest trying t[y_?NumericQ] := .... See mathematica.stackexchange.com/questions/18393/… for more information. -- oh, and be sure to ClearAll[t] before trying the ?NumericQ fix. -- and thanks for editing the question. – Michael E2 Jul 15 '15 at 1:52

Thank you Michael!! I will write the answer here for other people.

t[y_?NumericQ] := x /. FindRoot[g[x, y], {x, 1}]


worked like charm

• First @ FindRoot will have your function return a number instead of a list. – J. M. will be back soon Jul 15 '15 at 2:11

For multiple results you could do for example:

g1[x_, y_, z_] := 2 x + y - z
g2[x_, y_, z_] := x^2 - y^3 - z^2
t[x_] := t[x] = {y, z} /. FindRoot[{g1[x, y, z], g2[x, y, z]}, {{y, 1}, {z, 1}}]
Plot[{t[x][], t[x][]}, {x, 1, 5}, PlotStyle -> {Red, Green}] ContourPlot3D[{g1[x, y, z] == 0, g2[x, y, z] == 0}, {x, 0, 5}, {y, 0, -5}, {z, 0, 5}] 