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
A special thanks goes out to the (mathematica.stackexchange.com/questions/307564/how-to-speed-up-a-code-which-uses-findroot-in-a-plot)Stackexchange community

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warning-messages equation-solving performance-tuning




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