More Applications of Derivatives 175
Types of Tangent Lines
Horizontal Tangents:
(
dy
dx
= 0
)
. (See Figure 9.1-1.)
Figure 9.1-1
Vertical Tangents:
(
dy
dx
does not exist, but
dx
dy
= 0
)
. (See Figure 9.1-2.)
Figure 9.1-2
Parallel Tangents:
(
dy
dx
∣
∣∣
∣x=a=
dy
dx
∣
∣∣
∣x=c
)
. (See Figure 9.1-3.)
x = a
x = c
Figure 9.1-3
Example 1
Write an equation of the line tangent to the graph ofy =−3 sin 2x atx=
π
2
. (See
Figure 9.1-4.)