Question

Find the average rate of change of over the interval (0,9 ]

Answer 1

3. 10/9

4. 34

Explanation:

The average rate of change of f(x) over the interval a ≤ x ≤ b is:

`\sf (f(b)-f(a))/(b-a)`

Problem 3

Given interval: 0 ≤ x ≤ 9

From inspection of the graph:

• f(0) = -7
• f(9) = 3

`\sf average \ rate \ of \ change=(f(9)-f(0))/(9-0)=(3-(-7))/(9)=(10)/(9)`

Problem 4

Given:

• function f(x) = x³ - 9x
• interval: 1 ≤ x ≤ 6

⇒ f(1) = (1)³ - 9(1) = -8

⇒ f(6) = (6)³ - 9(6) = 162

`\sf average \ rate \ of \ change=(f(6)-f(1))/(6-1)=(162-(-8))/(5)=34`