Question 68
Find all pairs of twice differentiable functions $f, g : \mathbb{R} \to \mathbb{R}$, such that $f''$ and $g''$ are continuous, such that
$$
(f(x) - g(y)) \cdot (f'(x) - g'(y)) \cdot (f''(x) - g''(y)) = 0,
$$
for all $x, y \in \mathbb{R}$.
$$
(f(x) - g(y)) \cdot (f'(x) - g'(y)) \cdot (f''(x) - g''(y)) = 0,
$$
for all $x, y \in \mathbb{R}$.