How to find deriative y = f'(x) of a function y=f(x) with a given graph?

Question

like a graph like this (pretend that it is f(x)

http://demonstrations.wolfram.com/PolynomialGraphGenerator/HTMLImages/index.en/popup_4.jpg

how do we create the f'(x) graph, how to find slopes....

Answer 1

Well, the way to make an approximate f '(x) graph is like you said, to look at all the possible slopes of f(x).  The graph of    f '(x) is basically a graph of the slopes of f(x)

Increasing slopes on the f(x) graph show where the f '(x) graph is positive (above the x axis), and decreasing slopes on f(x) will show where the      f '(x) graph is negative (below the x axis).  Every local max and min on f(x) is going to be where the graph of f '(x) crosses the x axis.  

So at a local max on f(x), where the graph is a hump, opening downward, the slope of f(x) will change from increasing, to zero, to decreasing.  The graph of f '(x) at that point will change from positive, to 0, to negative.