Finding the extremum condition of the definite integral involving absolute function

Question

Let the differentiable function $f(x)>0$ be monotonically decreasing on the closed interval $[a, b]\subset \textbf{R}^{+}$. For $k>0$, does the integral $\int_{a}^{b} |f(x)-kx|\,\mathrm dx$ attain an extremum? If it does, when does it?