Barrons AP Calculus

Figure  N3–4

E2. Graphically

If we have the graph of a function f (x), we can use it to graph f ′(x). We
accomplish this by estimating the slope of the graph of f (x) at enough points to
assure a smooth curve for f ′(x). In Figure N3–5 we see the graph of y = f (x).
Below it is a table of the approximate slopes estimated from the graph.

Figure  N3–5

Figure N3–6 was obtained by plotting the points from the table of slopes
above and drawing a smooth curve through these points. The result is the graph