Answer:
The average rate of change of the function f(x) is 0.2
The coordinates of the end of the interval are (9 , 4)
Step-by-step 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 [tex]\frac{f(b)-f(a)}{b-a}[/tex]
* Lets solve the problem
∵ The function f(x) = √x + 1
∵ The interval of the function is 4 ≤ x ≤ 9
∵ The average rate = [tex]\frac{f(b)-f(a)}{b-a}[/tex] 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) = [tex]\frac{f(4-3}{9-4}[/tex]
∴ The average rate of change of f(x) = [tex]\frac{1}{5}[/tex] = 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)
