Consider the following optimization problem:
\begin{equation} \begin{aligned} \max_{x} & \quad f(x)g(x) \\ s.t. & \quad x \in [0, C] \end{aligned} \end{equation}
where $f: \mathbb{R} \to \mathbb{R}$ is a concave and nondecreasing function (maybe not differentiable at finitely many points) and $g: \mathbb{R} \to [0, 1]$ is a decreasing function. $C$ is a positive constant.
Is there any efficient algorithm for such a problem?