5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book April 11, 2018 15:14

208 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 10.1-10.)

(x 1 , y 1 )

Normal line

Tangent

f

Figure 10.1-10

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 10.1-11.)

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

Tangent Tangent Tangent

Normal

f

Normal

Normal

ff

Figure 10.1-11

(See Figure 10.1-12.)

At these points,mtangentdoes not exist; however,mnormal=0.