Author 
Comment/Response 
Josh Gray

05/25/12 1:10pm
I have the function:
ff[x_] := (Sin[x] + Tanh[x])/(1 + Sin[x] Tanh[x])
And I want to plot, find, and give the exact values of the intervals where the function is decreasing/increasing. This is what I did to start, first I took the derivative, then plotted:
In :D[ff[x], x]
Out:
(((Sin[x] + Tanh[x]) (Sech[x]^2 Sin[x] + Cos[x] Tanh[x]))/(1 +
Sin[x] Tanh[x])^2) + (Cos[x] + Sech[x]^2)/(1 + Sin[x] Tanh[x])
In:
Plot[(((Sin[x] + Tanh[x])*(Sech[x]^2*Sin[x] + Cos[x]*Tanh[x]))/(1 +
Sin[x]*Tanh[x])^2) + (Cos[x] + Sech[x]^2)/(1 +
Sin[x]*Tanh[x]), {x, 12, 12}, PlotRange > {.05, .05}]
Now I fun into how to place intervals of maybe colored lines on my graph to match where it is increasing/decreasing. Also I am not sure of any commands where I could pump out exact values where this is happening, help please? Some good explanation would be the most helpful maybe walking me like a baby through its first steps! This is due to me being new to mathematica
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