5 Steps to a 5 AP Calculus BC 2019

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.)