Page 298 - DMTH201_Basic Mathematics-1

Unit 11: Parametric Differentiation

For completeness, a graph of this curve is shown in Figure 11.3. Notes
Figure 11.3

dy
2
3
Example: Suppose we wish to find when x = t and y = t t.
dx
In this Example we shall plot a graph of the curve for values of t between 2 and 2 by first
producing a table of values (Table 11.2).
Table 11.2

Part of the curve is shown in Figure 11.4. It looks as though there may be a turning point
between 0 and 1. We can explore this further using parametric differentiation.

Figure 11.4

From

2
x = t 3 y = t t
we differentiate with respect to t to produce

dx dy
= 3t 2 = 2t 1
dt dt

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