I have a convex function of the form $f(x) = a + \frac{b}{x} + cx^2$ where $a, b,c$ are parameters. I need to find $a,b,c$ such that the resulting approximation function $f(x)$ is monotonic decreasing when x is in the range [0,50]. How can I find the $a,b,c$?
EDIT: I started like this:
$dy/dx < 0 $
$ -b+ 2cx^3 < 0 $ in the domain [0,50]
I am not sure,how do I solve for b and c? I am new to these kinds of problems and so a detailed explanation would be helpful. Thanks in advance!