When dP/dt is zero it is not increasing or decreasing, and when dP/dt<0 it is decreasing. Otherwise it is increasing and dP/dt>0.
So the turning point of neither increase or decrease is dP/dt=0 and rP(1-P/k)=0. Since rP cannot be zero or negative for an existing population P, 1-P/k=0 so P=k, the carrying capacity. If P<k, then 1-P/k>0 and the population increases because dP/dt>0. If P>k, 1-P/k<0 and dP/dt<0 and the population decreases. So if P does not exceed (or equal) its carrying capacity the population increases.