01/10/2023, 11:43
01/10/2023, 12:03
01/10/2023, 12:29
f[x_] := E^(4 - 2 x - 2 E^(2 - 2 x) x) x - x
sol = NSolve[f[x] == 0, Reals]
Plot[f[x], {x, -0.02, 2.3}, AxesLabel -> {"x", "f(x)"},
Epilog -> {Red, PointSize[Medium], Point[{x, f[x]} /. sol]}]
{{x -> 0.}, {x -> 1.}}
f[x_] := E^(4 - 2 x - 2 E^(2 - 2 x) x) x - x
{ref, imf} = ComplexExpand@ReIm@f[u + I v];
sol = NSolve@{ref == 0, imf == 0, -3/5 < u < 3/5, -3/5 < v < 3/5};
Transpose@{Thread@x -> u + I v /. sol}
ContourPlot[{ref == 0, imf == 0}, {u, -3/5, 3/5}, {v, -3/5, 3/5}, FrameLabel -> {"u", "v"},
Epilog -> {Red, PointSize[Medium], Point[{u, v} /. sol]}]
{{x -> 0}, {x -> -0.588173 - 0.502141 I}, {x -> -0.588173 + 0.502141 I}, {x -> -0.529697 - 0.493007 I}, {x -> -0.529697 + 0.493007 I}, {x -> -0.459626 - 0.481482 I}, {x -> -0.459626 + 0.481482 I}, {x -> -0.371817 + 0.466087 I}, {x -> -0.371817 - 0.466087 I}, {x -> -0.253118 - 0.443448 I}, {x -> -0.253118 + 0.443448 I}, {x -> -0.0647242 - 0.402666 I}, {x -> -0.0647242 + 0.402666 I}}
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