Question: New User - Symbolic differentiation to find Stationary point... PDF to CDF Definition


Hi all,

I have the following function:

phiS := (C,q) -> w*(int(a*f*g(x), x=0..a*f) + int(x*g(x), x=a*f..((w+pi2)*q-pi2*C)/w) + int(q*g(x), x=((w+pi2)*q-pi2*C)/w..infinity)) - s*q - pi1*(f-C) - pi2*int((C-q)*g(x), x=((w+pi2)*q-pi2*C)/w..infinity);

when I type the command:


I get the correct output (I've differentiated phiS on paper): pi1- pi2*int(g(x), x=((w+pi2)*q-pi2*C)/w..infinity);


My question is: how do I tell Maple that g(x) is a density function?  I'd like the result to have the following form: pi1 -pi2*[1-G((w+pi2)*q-pi2*C)/w)].  And then I'd like be able to set the above to zero, and get the stationary point. 


 IF there is a better way to do this, I'm completely open. 




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