Mathematics - Continuity - Differentiability Question with Solution | TestHub

Positivity lets us divide by $f(x-y)$. Taking difference quotients from the two sides as $y\to x$ forces $f^{\prime }(x)\le 0$ and $f\prime (x)\ge 0$. Thus $f^{\prime }\equiv 0$, so $f$ is constant and $f(5)=5$.