I have two functions defined on the same domain, $f(x)$ and $g(x)$ where $x$ is in $(0,1)$:
f[x_] := (-1 + x) Log[1 - x] - x Log[x] g[x_] := Log[1 + 2 (-1 + x) x]
I would like to find a constant $c$ such that the maximum of $f(x)-cg(x)$ is minimized on the domain $(0,1)$.
My first attempt was to try
but this just gives me back my input as the output.
Am I going about this the wrong way entirely? I feel like it's got something to do with the inner Maximize not evaluating because it's a function of more than one variable but I have no idea how to deal with this.