1. 7.2 Polynomial Functions and Their Graphs
Andrew Fisher 8-2

2. Local Minimum and Maximum
Local minimum and maximum are the highest and lowest points in their “neighborhood” on the graph.
2 points on either side of the minimum or maximum f(x1) and f(x2) are less than or greater than f(a).

3. Example
Find the Local Minimum and Maximum .

4. Answers
Local Minimum (-3,6) Local Maximum (3,-6)

5. Increasing and Decreasing Functions
F is increasing over an open interval if for every x1<x2 in the interval, f(x1)<f(x2) F is decreasing over an open interval if for every x1<x2 in the interval, f(x1)>f(x2)

6. End Behavior
F(x)=ax^n a>0 a<0 Left Right Left Right N is even Rise Rise Fall Fall N is odd Fall Rise Rise Fall

7. Find the End Behavior
x^ x^2
X^ x^5
2x^ x^3

8. Answers Rise on left 4. Fall on left Rise on right Fall on right
2. Fall on left Falls on left
Rise on right Rise on right
3.Rise on left Rise on left