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 $\displaystyle (B-2m)/A$ (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 $\displaystyle (B-2m)/A = 0$, what's true for $\displaystyle m=B/2$. This itself is a linear function with a negative slope, but the function is always positive before $\displaystyle m=B/2$. It starts from B and does down linearly untill $\displaystyle m=B/2$. So theoretically the overall function increases untill $\displaystyle m=B/2$, after this point, the partial derivative gets negative ($\displaystyle ((B-2m)/A)< 0$ for $\displaystyle m>B/2$) 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 $\displaystyle m=B/2$?

Thank you

Schdero