I saw somewhere an alternative definition of a derivative.. It's basically the same when calculating but when looking at the graph- well, it'd only be right if the function was in some way simetrical. Am I right? Or does this work for any function..

What I'm trying to say.. d(x1,x2) is not equal to 2d(x,x1) in any given function.?

( h's are not the same in x1, x2)

definition: (you have 3 points here instead of 2)

x

x1 = x+h

x2 = x-h

$\displaystyle f'(x) = \lim_{h\to0} \frac {f(x+h) - f(x-h)}{2h}$