Calculate the average rate of change for the following function given interval:
y=4x2−12x+9 over the interval [1, 2]
as usual, that would be
[y(2)-y(1)] / (2-1)
so plug and chug
Well, calculating the average rate of change is just like trying to calculate how fast your ice cream melts on a hot summer day. It's all about finding the difference in values and dividing by the difference in the "x" values.
So, let's dig into the math, shall we? We have the function y = 4x² - 12x + 9 over the interval [1, 2].
To find the average rate of change, we need to find the difference in y values and divide it by the difference in x values.
At x = 1, y = 4(1)² - 12(1) + 9 = 4 - 12 + 9 = 1.
At x = 2, y = 4(2)² - 12(2) + 9 = 16 - 24 + 9 = 1.
The difference in y values is 1 - 1 = 0.
The difference in x values is 2 - 1 = 1.
So, the average rate of change is 0/1 = 0.
Voilà! The average rate of change for the function over the interval [1, 2] is 0. So, it's like saying your ice cream won't melt at all. Enjoy your cold treat!
To calculate the average rate of change for a function over an interval, you need to find the difference in the values of the function at the endpoints of the interval and divide it by the difference in the inputs.
In this case, the function is y = 4x^2 - 12x + 9, and the interval is [1, 2].
To find the average rate of change, we need to find the difference in the values of the function at x = 1 and x = 2.
First, let's find the value of the function at x = 1:
y(1) = 4(1)^2 - 12(1) + 9 = 4 - 12 + 9 = 1
Next, let's find the value of the function at x = 2:
y(2) = 4(2)^2 - 12(2) + 9 = 16 - 24 + 9 = 1
Now, we can calculate the average rate of change:
Average Rate of Change = (y(2) - y(1)) / (2 - 1) = (1 - 1) / (1) = 0 / 1 = 0
Therefore, the average rate of change for the function y = 4x^2 - 12x + 9 over the interval [1, 2] is 0.
To calculate the average rate of change for the given function over the interval [1, 2], we need to find the difference in the function value at the endpoints of the interval and divide it by the difference in the input values.
First, let's find the function values at the endpoints of the interval [1, 2].
For x = 1:
y = 4(1)^2 - 12(1) + 9
= 4 - 12 + 9
= 1
For x = 2:
y = 4(2)^2 - 12(2) + 9
= 16 - 24 + 9
= 1
Next, let's find the difference in the function values:
Δy = y2 - y1
= 1 - 1
= 0
Now, let's find the difference in the input values:
Δx = x2 - x1
= 2 - 1
= 1
Finally, let's calculate the average rate of change:
Average rate of change = Δy / Δx
= 0 / 1
= 0
Therefore, the average rate of change for the function y = 4x^2 - 12x + 9 over the interval [1, 2] is 0.