What is the rate of change between the interval x=n and x = 3 pi/2?

The average rate of change of a continuous function,

f

(

x

)

, on the closed interval

[

a

,

b

]

is given by

f

(

b

)

-

f

(

a

)

b

-

a

Basically, the average rate of change tells us how, on average, the y-value of a function is changing per unit change in the x-value.

The average rate of change formula is just a variation of the slope formula

y

2

-

y

1

x

2

-

x

1

since

y

=

f

(

x

)

.

Let's let

f

(

x

)

=

-

x

2

+

8

x

-

9

.

The average rate of change on the closed interval

[

2

,

5

]

is given by

f

(

5

)

-

f

(

2

)

5

-

2

=

6

-

3

5

-

2

=

3

3

=

1