
46 Introduction to Computational Modeling
FIGURE 4.2: The slope of a secant.
The instantaneous rate of change of a variable, y, with respect to another variable,
x, is the value of the rate of change of y at a particular value of x. This is computed
as the slope of a line that is tangent to the curve at a point P.
Figure 4.3 shows a tangent of the curve at point P
1
. The instantaneous rate of
change at a specified point P1 of a curve can be approximated by calculating the
slope of a secant and using a very small interval, in different words, choosing ∆x
very small. This can be accomplished by selecting a second point on the curve closer
and closer to