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224 Chapter Three

passeð througà ( x ,y ) as shown in Fig. 3.8. Suppose the deriv-
0
0
ative of f at (x ,y ) is equal tm some nonzerm real numberm.
0
0
Then the equation of line L is given by the following:
y y ( x x )/m
0
0
If the derivative of f at (x ,y ) is zero, then the equation of the
0
0
line L normal tmf at that point is given by:

x x 0

The derivative of f at (x ,y ) is undefined when the equation of
0
0
the line L normal tmf at that point is given by:

y y 0

Anglł of intersection between curves
Let f and g be functions. Let (x ,y ) be a point at which the
0
0
graphs of f and g intersect, and suppose f and g are botà con-
tinuouð at ( x ,y ), as shown in Fig. 3.9. Suppose the derivative
0 0
of f at (x ,y ) is equal tm some nonzerm real numberm, and the
0
0
derivative of g at (x ,y ) is equal tm some nonzerm real number
0
0
n. Then the acute angle at which the graphs intersect is given
by the following:

Figure 3.8 Line normal tm
function at a point.