Find the average rate of change of f(x)=2x2−7 between each of the pairs of points below.
Between (3,11) and (6,65)
Between (b,m) and (s,u)
Between (x, f(x)) and (x+h, f(x+h))
Please help, I´m having trouble with that. I have done it in some diffrent ways and it kept telling me is wrong.
To find the average rate of change between two points, you need to calculate the difference in the function values and divide it by the difference in the x-values.
1. Between (3,11) and (6,65):
In this case, the x-values are 3 and 6, and the function values are 11 and 65, respectively.
The difference in function values is: 65 - 11 = 54.
The difference in the x-values is: 6 - 3 = 3.
Therefore, the average rate of change is: 54 / 3 = 18.
2. Between (b,m) and (s,u):
Here, the x-values are denoted by "b" and "s," and the function values are denoted by "m" and "u," respectively.
The difference in function values is: u - m.
The difference in the x-values is: s - b.
Therefore, the average rate of change is: (u - m) / (s - b).
3. Between (x, f(x)) and (x+h, f(x+h)):
This is a generalized form for finding the average rate of change between two points on any function.
The x-values are x and x + h, and the function values are f(x) and f(x + h), respectively.
The difference in function values is: f(x + h) - f(x).
The difference in the x-values is: (x + h) - x = h.
Therefore, the average rate of change is: (f(x + h) - f(x)) / h.
Please note that for the second and third cases, the exact values of the average rate of change cannot be determined without knowing the specific values of (b, m, s, u, x, f(x)).
To find the average rate of change of a function between two points, we need to calculate the difference in function values divided by the difference in x-values.
1. Between (3,11) and (6,65):
The x-values are 3 and 6, and the corresponding function values are 11 and 65 respectively.
The difference in function values = 65 - 11 = 54
The difference in x-values = 6 - 3 = 3
Therefore, the average rate of change = difference in function values / difference in x-values = 54 / 3 = 18.
2. Between (b,m) and (s,u):
Since the points are represented by variables, we need more information to calculate the average rate of change. Specifically, we need the values of b, m, s, and u. Once we have those values, we can follow the same steps as explained in the previous example.
3. Between (x, f(x)) and (x+h, f(x+h)):
The x-values are x and x+h, and the corresponding function values are f(x) and f(x+h) respectively.
The difference in function values = f(x+h) - f(x)
The difference in x-values = (x+h) - x = h
Therefore, the average rate of change = difference in function values / difference in x-values = (f(x+h) - f(x)) / h.
Make sure to substitute the actual function values and variables into the formula to obtain the specific average rate of change.
The average rate of change is
change-in-y
------------------
change-in-x
So, you have
Between (3,11) and (6,65): (65-11)/(6-3) = 54/3 = 18
(b,m) and (s,u): (u-m)/(s-b)
(x, f(x)) and (x+h, f(x+h))
[f(x+h)-f(x)]/h