Question

Use the following table of the function f(x) = x4 − 4x to answer this question:

x f(x)
-2 24
-1 5
0 0
1 -3
2 8
What is the average rate of change from x = −1 to x = 2?
A. −3
B. −1
C. 1
D. 3

Answer 1

`A(x) = (f(x) - f(a))/(x - a) = (f(-1) - f(2))/(-1 - 2) = (5 - 8)/(-3) = (-3)/(-3) = 1`
The answer is C.

Answer 2

we have

`f(x)=x^(4)-4x`

Step 1

Using the table find the value of f(x) for
`x=-1`

`x=-1\\f(-1)=5`

Step 2

Using the table find the value of f(x) for
`x=2`

`x=2\\f(2)=8`

Step 3

Find the average rate of change

we know that

the average rate of change is equal to the formula

`(f(b)-f(a))/(b-a)`

in this problem we have

`f(b)=f(2)=8`

`f(a)=f(-1)=5`

`b=2`

`a=-1`

substitute the values in the formula

`(8-5)/(2+1)`

`(3)/(3)=1`

therefore

the answer is the option C

the average rate of change is
`1`