5 Steps to a 5 AP Calculus BC 2019

180 STEP 4. Review the Knowledge You Need to Score High

Normal Lines

The normal line to the graph of f at the point (x 1 ,y 1 ) is the line perpendicular to the

tangent line at (x 1 ,y 1 ). (See Figure 9.1-10.)

(x 1 , y 1 )

Normal Line

Tangent

f

Figure 9.1-10

Note that the slope of the normal line and the slope of the tangent line at any point on the

curve are negative reciprocals, provided that both slopes exist.

(mnormal line)(mtangent line)=− 1.

Special Cases:

(See Figure 9.1-11.)

At these points,mtangent=0; butmnormaldoes not exist.

Tangent Tangent Tangent

Normal

f

Normal

Normal

f f

Figure 9.1-11

(See Figure 9.1-12.)

At these points,mtangentdoes not exist; howevermnormal=0.