The first kind of function is a constant function.
If f(x) = C for some constant C, then f'(x) = 0.
Constant functions have a slope of zero. On a graph, a constant function is a straight vertical line. It doesn't matter if we pick f(x) = 3 or f(x) = -10, or f(x) = π, or any other constant, the result would be the same. Zero. We like.