5 Steps to a 5 AP Calculus BC 2019

Graphs of Functions and Derivatives 115

concave

downward

f ′′< 0 f′′< 0

Figure 7.2-14

Figure 7.2-15

Points of Inflection
A point P on a curve is a point of inflection if:

1. the curve has a tangent line at P, and


2. the curve changes concavity at P (from concave upward to downward or from concave
   downward to upward).

(See Figures 7.2-16–7.2-18.)

f′′< 0

f′′> 0

pt. of inflection

Figure 7.2-16

f′′< 0

f ′′> 0

pt. of inflection

Figure 7.2-17

f′′> 0 f′′< 0

CUSP

not a pt. of

inflection

Figure 7.2-18