Question

Select the correct answer. If f(x)=x^3-x , what is the average rate of change of f(x) over the interval [1, 5]?

Answer 1

average rate of change = 30

Explanation:

the average rate of change of f ( x)

over an

interval between 2 points is the slope of the secant

line connecting the 2 points

It is calculated as

f

(

b

)

−

f

(

a

)

b

−

a

where a, b is the closed interval

[

a

,

b

]

here

[

a

,

b

]

=

[

1

,

5

]

f

(

b

)

=

f

(

5

)

=

5

3

−

5

=

120

f

(

a

)

=

f

(

1

)

=

1

−

1

=

0

⇒

120

−

0

5

−

1

=

120

4

=

30

Answer 2

Average rate of change = 30

Explanation:

We have given a function.

f(x) = x³-x

[a,b] = [1,5]

We have to calculate the average rate of change of f(x) over the given interval.

The formula to calculate the average rate of change of function is :

Average rate of change = f(b) - f(a) / (b-a)

f(b) = f(5) = (5)³-5

f(b) = f(5) = 125-5

f(b) = f(5) = 120

f(a) = f(1) = (1)³-1

f(a) = f(1) = 1-1

f(a) = f(1) = 0

Putting values in formula, we have

Average rate of change = 120-0 / 5-1

Average rate of change = 120/4

Average rate of change = 30 which is the answer.