How to plot the function f(x) so that one part be a ticker line than another depending on the value x?

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How to plot the function f(x) so that one part be a ticker line than another depending on the value x? (Curve is efficient frontier - portfolio optimization)

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f[x_] := x^2;
Show[
  Plot[f[x], {x, -1, 1}, PlotRange -> {{-1, 2}, {-1, 4}}], 
  Plot[f[x], {x, 1, 2}, PlotStyle -> Thickness[.02]]
]