Question

Select all the correct locations on the table.

Answer 1

Average rate of change: r=[f(b)-f(a)]/(b-a)

r=-60→[f(b)-f(a)]/(b-a)=-60

b=5; f(b)=-213; a=1; f(a)=27
(-213-27)/(5-1)=(-240)/4=-60

Answer: The two points in the table which create an interval with an average rate of change of -60 are:
x     f(x)
1      27
5   -213

Answer 2

Answer:

1 and 5

Step-by-step explanation:

Since, the rate of change of function f(x) between a to b is $\frac{f(b)-f(a)}{b-a}$ or $\frac{f(a)-f(b)}{a-b}$

Given,

f(1) = 27, f(2) = 21, f(3) = 3, f(4) = -51 and f(5) = -213,

Thus, the rate of change between 1 and 2 = $\frac{f(2)-f(1)}{2-1}=\frac{21-27}{2}=\frac{-6}{2}=-3$

Similarly,

The rate of change, between 1 and 3 = -12,

between  1 and 4 = -26,

between  1 and 5 = -60,

between  2 and 3 = -18,

between  2 and 4 = -36,

between 2 and 5 = 78,

between  3 and 4 = -54,

between  3 and 5 = -108,

between 4 and 5 = -162

Hence, the point in the table that create an interval with the rate of change -60 are,

1 and 5.