Generalized inflection points of very general line bundles on smooth curves

Let L be an invertible sheaf on a smooth curve C. A generalized inflection point of L is an inflection point of $$L^{\otimes n}$$ for some integer n > 0. A generalized inflection point P of L is called strongly normal if there is a unique integer n > 0 such that P is an inflection point of $$L^{\otimes n}$$ and moreover its inflection weight is equal to 1. In case L is a very general invertible sheaf of degree x on C then all generalized inflection points of L are strongly normal.