I know that f(x) is derivative at x=0, and I need to prove the following, while x<a<y :
Is this a proper proof? Thank you very much!
The problem is that you don't show how to go from one step to the next. The next to last line is $\displaystyle \lim_{x,y\to a}\frac{f(y)- f(x)}{y- x}$ and the line just before that is $\displaystyle \lim_{x,y\to a}\frac{f(x+ y- a)- f(x)}{y- x}$. How did you get from one to the other?