Solve for f(x) using both 4 and 8:
f(x) = 4+6 = 10
f(x) = 8+6 = 14
Find the difference between the answers:
The difference between the two answers is 14-10 = 4
Find the difference between the interval:
The difference between 4 and 8 is: 8-4 = 4
The rate of change is the change in the answers over the difference in the interval:
The rate of change is 4/4 = 1
Answer:
The Average rate of change for f(x) = x+6 over the interval (4,8) is 1
Solution:
We define the Average rate of function f(x) over the interval (a, b) as
[tex]\frac{f(b)-f(a)}{b-a}[/tex] --- eqn 1
From question, given that
f(x) =x+6 --- eqn 2
The interval is (4,8) .hence we say a = 4 and b = 8
The average rate of change for f(x) = x + 6 is given by using eqn 1
[tex]\frac{f(8)-f(4)}{8-4}[/tex] --- eqn 3
Where, by using eqn 2 , we get f(8) = 8+6 =14 and f(4) = 4+6 =10
Such that the required value would be f(8)-f(4) = 14-10 = 4
By substituting the values of f(8) and f(4) in eqn 3 ,the average rate of change for the given expression is
[tex]=\frac{14-10}{8-4}=\frac{4}{4}=1[/tex]
Hence the Average rate of change for f(x) = x+6 over the interval (4,8) is 1
