0
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The derivative can be used to calculate roots. However the same function cannot be plotted.The error is at start point of domain:

f[x_, lam_] := lam*(x - 1) (x - 3) (x - 5)/10
Plot[f[x, 3], {x, -1, 6}, PlotStyle -> {Thick, Purple}, GridLines -> Automatic]
Solve[D[f[x, 5], x] == 0, x]
Plot[D[f[x, 5], x], {x, -1, 6}, PlotStyle -> {Thick, Blue}, GridLines -> Automatic]
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  • $\begingroup$ Add Evaluated -> True to your second plot. $\endgroup$ – Öskå Oct 30 '14 at 18:18
  • $\begingroup$ Related: (6894) and many others. $\endgroup$ – Mr.Wizard Oct 30 '14 at 21:48

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