Numerical differentation - finding maxima

I was analyzing my data and made a graph of it ($ f(x)$) and I wanted to find the maxima of $ frac {df(x)}{dx} $.

The derivative of a function is defined as $;$ $f'(x) = lim_{h to 0} frac {f(x+h)-f(x)}{h}$

Well, I did the numerical differentation of my data in Origin which is more precise (I did it manually too). Then I found the maximal value of that. I picked the maxima from my numerical differentition list automically even though the data here had negative sign but I suppose I should take the absolute value of the numbers in that list if I am finding the point of my curve where the $f(x)$ change is the most rapid, right?

I know it is a trivial question but I somehow froze here.

An example: $f(x) = {f(x_0),f(x_1),f(x_2),f(x_3),f(x_4)}$ and $x = {x_0,x_1,x_2,x_3,x_4}$, then

$ frac {df(x)}{dx} = { frac {f(x_1)-f(x_0)}{x_1-x_0},frac {f(x_2)-f(x_1)}{x_2-x_1},frac {f(x_3)-f(x_2)}{x_3-x_2},frac {f(x_4)-f(x_3)}{x_4-x_3} }$ corresponds to ${-4, 1,0, 3}$

so the maxima of $ frac {df(x)}{dx} $ is $4$ right?