To find the average rate of change of the function y = 2e^x over the interval from x = 0 to x = 2, we use the formula for the average rate of change:
Average Rate of Change = (f(b) – f(a)) / (b – a)
Here, a = 0 and b = 2. First, we need to calculate f(0) and f(2):
- f(0) = 2e^0 = 2 * 1 = 2
- f(2) = 2e^2
Now we substitute these values into the average rate of change formula:
Average Rate of Change = (f(2) – f(0)) / (2 – 0)
So we have:
Average Rate of Change = (2e^2 – 2) / 2
Now, simplifying this expression:
Average Rate of Change = (2(e^2 – 1)) / 2 = e^2 – 1
Therefore, the average rate of change of the function y = 2e^x over the interval from x = 0 to x = 2 is e^2 – 1.