Mathematica: How to speed up a code which uses FindRoot in a plot?

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How to speed up a code which uses FindRoot in a plot?
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(mathematica.stackexchange.com/users/78049/codebpr)codebpr
(mathematica.stackexchange.com/users/29/rolf-mertig)Rolf Mertig
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warning-messages equation-solving performance-tuning




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