In words: If we change x by an amount dx,thene f changes by an amount df;the derivative
is the proportionality factor. For example. in Fig. 1.17(a),the function varies slowly with
x, and the derivative is correspondingly small. In Fig. l.l7(b), f increases rapidly with x,
and the derivative is large, as you move away from x = 0.
Geometrical Interpretation: The derivative df /dx is the slope of the graph of / versus x.