first of all, i am confused by the definition of . as i see it, this should be:
that is, we want to represent the change in h between the points and (x0 plus "a little bit more (plus/minus)"). what you have doesn't look right at ALL, since as , but the idea should be: "h changes very little, if x does".
writing similar definitions for :
this is almost what we want, the only "sticking point" is the term , so to finish the proof, one has to show that:
so that one can conclude: