The average rate of change of a function over an interval is calculated using the formula:
Average Rate of Change = (f(b) – f(a)) / (b – a)
In this case, we want to find the average rate of change of the function y = cos(2x) over the interval [0, π/2]. Here, a = 0 and b = π/2.
First, let’s calculate the values of the function at the endpoints:
- When x = 0:
- f(0) = cos(2 * 0) = cos(0) = 1
- When x = π/2:
- f(π/2) = cos(2 * (π/2)) = cos(π) = -1
Now, we can plug these values into our average rate of change formula:
Average Rate of Change = (f(π/2) – f(0)) / (π/2 – 0)
Average Rate of Change = (-1 – 1) / (π/2 – 0) = -2 / (π/2) = -4/π
Therefore, the average rate of change of y = cos(2x) on the interval [0, π/2] is -4/π.