Question

the table shows some values of a function f(x).
x | f(x)
0 | 8
1 | 2
2 | -7
3 | -11
on which interval is the function decreasing the fastest?
0 < x < 1
1 < x < 2
2 < x < 3

Explanation:

Step1: Calculate rate for 0<x<1

$\text{Average rate} = \frac{f(1)-f(0)}{1-0} = \frac{2-8}{1} = -6$

Step2: Calculate rate for 1<x<2

$\text{Average rate} = \frac{f(2)-f(1)}{2-1} = \frac{-7-2}{1} = -9$

Step3: Calculate rate for 2<x<3

$\text{Average rate} = \frac{f(3)-f(2)}{3-2} = \frac{-11-(-7)}{1} = -4$

Step4: Compare magnitude of rates

The most negative value is -9, so the interval with the fastest decrease is where this rate occurs.

Answer:

$1 < x < 2$