Maximum, function with three variables
I have a function, which encompassed formerly two variables and three constants. I found the maximum of this function. For some analysis I'm doing, I have to make one of the constants a variable though.
If i do the partial derivative regarding the new variable, i get (A,B = constants; m = variable; A,B,m >0; m<B). I wonder now, where the maximum of this new function with three variables is.
What i did is i set , what's true for . This itself is a linear function with a negative slope, but the function is always positive before . It starts from B and does down linearly untill . So theoretically the overall function increases untill , after this point, the partial derivative gets negative ( for ) and henceforth starts from then on decreasing the overall function.
Is it correct that i thus say, the maximum of the function with three varibales is the same as the one with two, except for ?