On page 52 of What Sustains Social Norms and How They Evolve?, Assumption 1 is as follows:
Assumption 1: $d$ is continuously differentiable, $d'(x) \ge 0$ for all $x<0$ and $d'(x) \leq 0$ for all $x>0$ (it follows that $d'(0)=0$).
I don't understand the use of $\ge$ and $\le$ here. If $d'(0)=0$ implies a maximum is obtained at $x=0$, then every $x$ to the left of $0$ should have a strictly positive derivative and every $x$ to the right of $0$ should have a strictly negative derivative (i.e., $>$ and $<$ should be used).
What is the meaning behind $d'(x) \ge 0$ and $d'(x) \le 0$?
Edit: $d(g-\eta)$ is a function representing the disutility from social disapproval, where $g$ is a tip at a restaurant as a percentage of the bill and $\eta$ is the norm tip. The consumer takes as given $\eta$ (i.e., the social norm) and chooses $g$ to minimise the social disutility $d(x)$; i.e, bring it closer to $0$, where $x=g-\eta$.
Note: there is a trade-off to minimising $d$ that is probably not necessary to understand for my question.