Thread: Maximum, function with three variables

Hi everybody!
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 ?

Thank you

Schdero

Originally Posted by Schdero

Hi everybody!
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.

Partial derivative of what?

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 ?

Thank you

Schdero

You need to post sufficient information so that we can see what exactly you are talking about.

CB

Overall Function=

Maximum of the function f(a,c) is at a and c = infinity, as then fa=0 fc=0, (faa)(fcc)-fac^2 > 0.

Is there any further information you need to judge the corectness of my implication, that the maximum of f(a,c,m) lies at a and c = infinity, m=b/2?

Originally Posted by Schdero

Overall Function=

Maximum of the function f(a,c) is at a and c = infinity, as then fa=0 fc=0, (faa)(fcc)-fac^2 > 0.

Is there any further information you need to judge the corectness of my implication, that the maximum of f(a,c,m) lies at a and c = infinity, m=b/2?

What is the function you are trying to maximise, and what are the vaiables and constraints?

CB