# FINDING AVERAGE AND INSTANTENOUS RATE OF CHANGE WORKSHEET

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

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? (1)-32 (2) 64 (3) -76 (4) -1

Solution

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

Problem 4 :

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

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

1)

1)  3/5 feet/min

2)  7/12 feet/min

3)  -11 feet/min

2)  -3/2

3)  h(x) > f(x) > g(x)

4)  3.3 feet/sec

5)  4 glasses/hour

6)  -0.04

For the following exercises, find the average rate of change of each function on the interval specified.

Problem 1 :

f(x) = x2 + 2 on [-1, 2]

Solution

Problem 2 :

f(x) = 4x2 - 7 on [1, b]

Solution

Problem 3 :

g(x) = 2x2 - 9 on [4, b]

Solution

For each problem, find the average rate of change of the function over the given interval. You may use the provided graph to sketch the function.

Problem 4 :

f(x) = x2 - 2x + 1; [0, 1/3]

Solution

Problem 5 :

Solution

Problem 6 :

Solution

Problem 7 :

f(x) = -x+ 1; [-1, -3/4]

Solution

1)  average rate of change = 1

2) average rate of change = 4(b + 1)

3)  average rate of change = 2(b + 4)

4) Average rate of change = -5/3

5)  Average rate of change = -2/9

6) Average rate of change = -1/34

7)  Average rate of change = 7/4

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