What is the average rate of change of the function g(x) = 3(2x) - 6 over the interval 0<=x<=3? Show all work.
To find the average rate of change of a function over a given interval, we need to determine the difference in values of the function at the interval endpoints and divide it by the difference in the values of x at those endpoints.
First, let's find the value of g(x) at the lower endpoint, x = 0:
g(0) = 3(2(0)) - 6
= 3(0) - 6
= 0 - 6
= -6
Next, let's find the value of g(x) at the upper endpoint, x = 3:
g(3) = 3(2(3)) - 6
= 3(6) - 6
= 18 - 6
= 12
Now, we can calculate the difference in the function values:
g(3) - g(0) = 12 - (-6)
= 12 + 6
= 18
Next, let's calculate the difference in the x-values:
3 - 0 = 3
Finally, we can calculate the average rate of change:
Average Rate of Change = (g(3) - g(0)) / (3 - 0)
= 18 / 3
= 6
Therefore, the average rate of change of the function g(x) = 3(2x) - 6 over the interval 0 ≤ x ≤ 3 is 6.
To find the average rate of change of the function g(x) = 3(2x) - 6 over the interval 0 <= x <= 3, we need to find the difference in the function values at the endpoints of the interval and divide it by the difference in the input values.
First, let's evaluate the function at the endpoints of the interval:
- For x = 0:
g(0) = 3(2(0)) - 6 = -6
- For x = 3:
g(3) = 3(2(3)) - 6 = 12 - 6 = 6
The function values at the endpoints are -6 and 6.
Now, let's find the difference in function values:
Difference in function values = g(3) - g(0) = 6 - (-6) = 6 + 6 = 12
Next, let's find the difference in the input values:
Difference in input values = 3 - 0 = 3
Finally, let's calculate the average rate of change by dividing the difference in function values by the difference in input values:
Average rate of change = (Difference in function values) / (Difference in input values) = 12 / 3 = 4
Therefore, the average rate of change of the function g(x) = 3(2x) - 6 over the interval 0 <= x <= 3 is 4.
that would be
(g(3)-g(0))/(3-0)
now just plug in your values.