Average Rate of Change: Exploring More Functions

functions

-

2

x

+ 4 x + 5

3

x

- 6

2

x

+ 5 x + 12

4

x

8

-

2

x

+ 1

3 x

-0.5x



2

1+61

-1.1x



x

0

1

Δx

1

m, the average rate of change

This Demonstration shows the average rate of change for different

x

0

and

Δx

values for polynomial functions of degree 2, 3, and 4, an exponential function, and a logistic function.

Choose the polynomial of degree four and

Δx=0.5

. Select

x

0

from -2.8 to 2.8. Make a table for the

x

intervals in which

m

is negative, zero, or positive.

What is the orientation of the secant line (increasing, decreasing or horizontal) when

m

is negative, zero, or positive?

You found a relationship between the

m

value and the position of the secant line. Is this relationship also correct for the exponential function

3x

-0.5x



?