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

Answer:

Option c) 8 is the answer.

Step-by-step 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 = $\frac{\delta f(x)}{\delta x}$

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 = $\frac{40}{5}=8$

Option C is the answer.