Question

What is the average rate of change of f(x), represented by the table of values, over the interval [-3, 4]?

x f(x)
-6 27
-3 6
-1 2
0 3
1 6
4 27

Answer 1

The average rate of change (A(x)) of f(x) over interval [a, b] is given by:

`A(x) = (f(b)-f(a))/(b-a)` ......[1]

As per the statement:

Given the table:

x f(x)

-6 27

-3 6

-1 2

0 3

1 6

4 27

We have to find the average rate of change of f(x), represented by the table of values, over the interval [-3, 4].

At x = -3

then;

f(-3) = 6

At x = 4

then;

f(4) = 27

Substitute the given values in [1] we have;

`A(x) = (f(4)-f(-3))/(4-(-3))`

⇒
`A(x) = (27-6)/(7) = (21)/(7) = 3`

Therefore, the average rate of change of f(x), represented by the table of values, over the interval [-3, 4] is, 3

Answer 2

Average rate of change = (f(b) - f(a))/(b - a) = (f(4) - f(-3))/(4 - (-3)) = (27 - 6)/(4 + 3) = 21/7 = 3