Use the table to calculate the average rate of change of f(x) over the interval [0,4].
x f(x)
-4 1
-3 2
-2 4
-1 8
0 16
1 32
2 64
3 128
4 256
Wow, that's quite an exponential growth we have there! Anyway, to calculate the average rate of change of f(x) over the interval [0,4], we need to compare the change in f(x) with the change in x.
The change in f(x) from x = 0 to x = 4 is f(4) - f(0) = 256 - 16 = 240.
The change in x from x = 0 to x = 4 is 4 - 0 = 4.
Now we can calculate the average rate of change:
Average Rate of Change = (Change in f(x))/(Change in x)
= 240/4
= 60
So, the average rate of change of f(x) over the interval [0,4] is 60. Keep in mind that f(x) is growing exponentially, so that's quite the growth spurt!
To calculate the average rate of change of f(x) over the interval [0,4], you can use the formula:
Average rate of change = (f(b) - f(a)) / (b - a)
where b = 4 and a = 0.
So, f(b) = f(4) = 256
and f(a) = f(0) = 16
Substituting these values into the formula, we get:
Average rate of change = (256 - 16) / (4 - 0)
Simplifying further, we have:
Average rate of change = 240 / 4
Therefore, the average rate of change of f(x) over the interval [0,4] is 60.
To calculate the average rate of change of a function over an interval, you need to find the difference in the function values divided by the difference in the x-values.
In this case, the function f(x) is given in the table. And we need to find the average rate of change of f(x) over the interval [0,4].
To do this, we will first find the difference in the function values (f(x)) for the endpoints of the interval, and then divide it by the difference in the x-values.
The x-values for the interval [0,4] are 0 and 4.
So, the difference in the x-values = 4 - 0 = 4.
Now, let's find the difference in the function values (f(x)) for the endpoints.
For x = 0, f(x) = 16.
For x = 4, f(x) = 256.
The difference in the function values = 256 - 16 = 240.
Finally, we divide the difference in the function values by the difference in the x-values to find the average rate of change:
Average rate of change = difference in function values / difference in x-values = 240 / 4 = 60.
Therefore, the average rate of change of f(x) over the interval [0,4] is 60.
all you need are the values at the ends of the interval. That is,
(f(4)-f(0))/(4-0)