I have a function of multiple variables (5 to be exact). I would like to know if this function is positive or negative given certain constraints on each of the 5 variables. Here is a simplified example:
f[a_,b_,c_,d_,e_] := (2a-b+(c^2)+d-(e*a)) / ((b+c-e)^2)
Is this positive or negative, given
a>=1, b>=1, c>=1, 0<=d<=1, 0<=e<=1
I know there are tests such as Positive, but I'm unsure how to add constraints into those given that this is a mess of variables.
My example is relatively easy to do by hand, but the reality of my particular formula is much more complex. I feel that there is a way to do this, and further, for Mathematica to tell me if there is a range of each variable value over which the function is positive or negative.
Thank you for any assistance you can provide!