Manipulate[g = d^3 - C0*d + 2;
sol = NSolve[g == 0 && -4 < d < 4, d, Reals];
Column[{StringForm["C0=`` and Roots=``.", C0, d /. sol],
Plot[g, {d, -4, 4}, ImageSize -> 300,
Epilog -> {PointSize[0.02],
Point[Transpose[{d /. sol, g /. sol}]]},
PlotRange -> {-15, 15}]}], {{C0, 3.5}, 0, 10}]
Or:
f[x_, c_] := x^3 - c*x + 2
Manipulate[roots = x /. NSolve[f[x, C0] == 0, x];
pts = Select[{#, 0} & /@ roots, Element[#[[1]], Reals] &] // Union;
{xmin, xmax} = If[Length[pts] > 1, MinMax[pts[[All, 1]]], {-2, 2}];
Column[{StringForm["C0=`` and Roots=``.", C0, d /. sol],
Plot[f[x, C0], {x, xmin, xmax},
Epilog -> If[Length[pts] > 0, {Red, AbsolutePointSize[6], Point[pts]}, {}],
ImageSize -> 500]}],
Grid[{{Control[{{C0, 0}, 0, 10, 0.1, Appearance -> "Labeled"}]}}]]
Regards MI.