I am trying to do symbolic maximization of a function, and would like to specify the range of a parameter of that function.
I am able to set constraints of the variable I am maximizing over, but am not sure how to set constraints/range for a variable I am not maximizing over.
Here I would like to specify that a is always positive. How can I do that? And can this be done globally?
Maximize[{x^0.5 - a*x, x > 0}, x]
Thanks!
EDIT
A slightly more complicated example, where I am stuck: if I want to specify the exponent symbolically, and want to put a constraint on it (say $0<b<1$?)
Maximize[{x^b - a*x, x > 0}, x]