MA 3972-MA-Book April 11, 2018 15:14
More Applications of Derivatives 203Types of Tangent Lines
Horizontal Tangents:
(
dy
dx= 0
). (See Figure 10.1-1.)
Figure 10.1-1Vertical Tangents:
(
dy
dx
does not exist but
dx
dy= 0
). (See Figure 10.1-2.)
Figure 10.1-2Parallel Tangents:
(
dy
dx∣
∣∣
∣x=a=dy
dx∣
∣∣
∣x=c). (See Figure 10.1-3.)
x = a
x = cFigure 10.1-3Example 1
Write an equation of the line tangent to the graph ofy=−3 sin 2xatx=
π
2
.
(See Figure 10.1-4.)