FINDING AVERAGE OR INSTANTANEOUS RATE OF CHANGE FROM A TABLE

Problem 1 :

Use the following table to find the average rate of change on the given interval.

1. [3, 13]

2. 0 ≤ x ≤ 12

3. [3, 4]

Solution:

1. [3, 13]

2. 0 ≤ x ≤ 12

3. [3, 4]

Problem 2 :

The function h(x) is given in the table below. Which of the following choices shows the average rate of change of the function over the interval 2 ≤ x ≤ 6?

Solution:

So, option (1) is correct.

Problem 3 :

Given the functions g(x), f(x) and h(x) shown below.

The correct list of functions ordered from greatest to least by average rate of change over the interval 0 ≤ x ≤ 3 is

A. f(x), g(x), h(x)        B. h(x), g(x), f(x)  

C. g(x), f(x), h(x)        D. h(x), f(x), g(x)

Solution:

g(x) = x² - 2x

For the average rate of change of a function between x = 0 and x = 3.

For the function 'g',

g(x) = x² - 2x

g(3) = 3² - 2(3)

= 9 - 6

= 3

g(0) = 0² - 2(0)

= 0

h(3) = 9

h(0) = 2

Therefore, order of rate of change from greatest to the least for the given functions will be,

h(x) > f(x) > g(x)

So, option (D) is correct.

Problem 4 :

Use the table below to estimate the value of d'(120). Indicate units of measures.

Solution:

d'(120) = 180 - 60

Problem 5 :

Frank is selling lemonade. The function g(t) = (t² + 4)/2 models the number of glasses he sold, g(t), after t hours. What is the average rate of change between hour 2 and hour 6? Show all work.

Solution:

Problem 6 :

The table shows the average diameter of a person's pupil as a person ages. What is the average rate of change of a person's average pupil diameter from age 30 to 70? Be sure to include units.

Solution: