Question: Different colours for piecewise function

Hello,

 

I'm trying to plot the function (5*x)/(x^2-4) highlighting all of its characteristics (maxima, minima, convexity, concavity...). I would like to plot this function in different colors in accordance with the different intervals of concavity and convexity. In order to do this, I have tried to use the piecewise function, as shown on another question (http://www.mapleprimes.com/posts/43593-Piecewise--Color). However, I feel I haven't understood quite well how it works, as I can't figure out how to write the intervals... I don't know if I should show you my attempt, but I think it's quite ridiculous (I just have tried to adapt it to the example shown on the question I have read).

 

Thank you very much for your attention!

 

Have a nice day!

 

Skyblue

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