Question

Find the average rate of change of the function f (x) = StartRoot x EndRoot + 1 on the interval 4 ≤ x ≤ 9. Recall that the coordinates for the start of the interval are (4, 3).

What are the coordinates for the end of the interval?

Answer 1

What are the coordinates for the end of the interval?

(9,4)

What is the average rate of change for this function on the given interval?

1/5

Correct of edge 2020

Explanation:

Just took the quiz

Answer 2

The average rate of change of the function f(x) is 0.2

The coordinates of the end of the interval are (9 , 4)

Explanation:

* Lets explain how to solve the problem

- We can calculate the average rat of change of a function f(x) on

interval [a , b] by using the rule
`(f(b)-f(a))/(b-a)`

* Lets solve the problem

∵ The function f(x) = √x + 1

∵ The interval of the function is 4 ≤ x ≤ 9

∵ The average rate =
`(f(b)-f(a))/(b-a)` on the interval

[a , b] ⇒ (a ≤ x ≤ b)

∴ a = 4 and b = 9

∴ f(4) = √4 + 1 = 2 + 1 = 3

∴ f(9) = √9 + 1 = 3 + 1 = 4

∴ The average rate of change of f(x) =
`(f(4-3)/(9-4)`

∴ The average rate of change of f(x) =
`(1)/(5)` = 0.2

* The average rate of change of the function f(x) is 0.2

∵ f(4) = 3

∵ f(9) = 4

∵ f(x) on the interval 4 ≤ x ≤ 9

∵ The coordinates of the start of the interval are (4 , 3)

∴ The coordinates of the end of the interval are (9 , 4)