# Find the root of a function with two variables?

Posted 11 months ago
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 I have this equation : w[s_, u_] := 1 + (1 + 0.65 s - 1.2 s^2 - 0.4 s^3 + 0.35 s^4) Cos[u] + (1.4 s - 0.4 s^2 - 1.5 s^3 - 0.35 s^4) Sin[u]; And I need to find the critical point of this equation; The requirement is using the ContourPlot and FindRoot to solve it, so I need to give the FindRoot function an initial guess for a critical point; I can see the initial guess now, but how to find the "Find Root function" ?If I try: FindRoot[w[s, u], {s, 0}, {u, pi}] ,then the error message: " The number of equations does not match the number of variables in FindRoot[w[s,u],{s,0},{u,[Pi]}]."Please help, Thank you!
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Posted 11 months ago
 In this case I would try FindMaximum: FindMaximum[w[s, u], {s, .3}, {u, .1}] For exact symbolic solutions you can use Reduce: Reduce[Grad[Rationalize[w[s, u]], {s, u}] == 0 && -1 < s < 1 && -1 < u < 1, {s, u}, Reals] % // N 
 It is not w that you want to be zero, but its gradient: FindRoot[Grad[w[s, u], {s, u}] == 0, {s, 0}, {u, Pi}]