Answer:
The average rate of change of is 12
The average rate of change of is 10
Step-by-step explanation:
The average rate of change of f(x) over an interval between 2 points (a ,f(a)) and (b ,f(b)) is the slope of the secant line connecting the 2 points.
We can calculate the average rate of change between the 2 points by
-------------------(1)
(1) The average rate of change of the function over the interval 1
≤
x
≤
5
f(a) = f(1)
f(1) =1+6+13
f(a) = 20---------------------(2)
f(b) = f(5)
f(5) = 25 +30 +13
f(5) = 68-----------------------(3)
The average rate of change between (1 ,20) and (5 ,68 ) is
Substituting eq(2) and(3) in (1)
=
=
=
=12
This means that the average of all the slopes of lines tangent to the graph of f(x) between (1 ,20) and (5 ,68 ) is 12
(2) The average rate of change of the function over the interval -1
≤
x
≤
5
f(a) = f(-1)
f(1) =1-6+13
f(1) = 8---------------------(4)
f(b) = f(5)
f(5) = 25 +30 +13
f(5) = 68-----------------------(5)
The average rate of change between (-1 ,8) and (5 ,68 ) is
Equation (1) becomes
On substituting the values
=
=
=
= 10
This means that the average of all the slopes of lines tangent to the graph of f(x) between (-1 ,8) and (5 ,68 ) is 10