# utility – Intuition for proper monotne functions

While reading documents about utility theory, I came across a definition of a suitable monotonous function, which is a function with $$u & # 39;> 0$$, $$u & # 39; & # 39; <0$$, $$u & # 39; & # 39; & # 39;> 0$$ and so.
The first conditions are clear: more is better than less and marginal utility decreases. I am not sure how to interpret the higher order conditions and, in general, what is "appropriate" about this function?

Any intuition is appreciated.