Question

What is the average rate of change of f(x), represented by the table of values, over the interval [-3, 2]?

x | f(x)
-5 -150
-3 -36
-1 -2
0 0
1 0
2 4


a) -40
b) -8
c) 8
d)32

Answer 1

a)-40 is the correct answer

Answer 2

Option c) 8 is the answer.

Explanation:

Given table is

x -5 -3 -1 0 1 2

f(x) -150 -36 -2 0 0 4

We have to find the rate of change of f(x) over the period of x [-3, 2]

Since rate of change of x =
`(\delta f(x))/(\delta x)`

Now we have been given
`\delta x=x_(2)-x_(1)`

and
`\delta x=2-(-3)=5`

Similarly
`\delta f(x)=f(x_(2))-f(x_(1))`

`\delta f(x)=36-(-4)=36+4=40`

Now rate of change of f(x) will be =
`(40)/(5)=8`

Option C is the answer.