Step-by-step explanation:
To find the average rate of change of a function over an interval, you can use the formula:
Average Rate of Change = (f(b) - f(a)) / (b - a)
Where:
- f(b) is the value of the function at the end of the interval
- f(a) is the value of the function at the beginning of the interval
- b is the end of the interval
- a is the beginning of the interval
For the cosine function, we have:
f(x) = cos(x)
Given the interval from 5π/6 to 4π/3:
a = 5π/6
b = 4π/3
Now, let's find the values of the cosine function at these points:
f(a) = cos(5π/6)
f(b) = cos(4π/3)
Then, we can calculate the average rate of change:
Average Rate of Change = (cos(4π/3) - cos(5π/6)) / ((4π/3) - (5π/6))
You can simplify this expression to find the numerical value of the average rate of change.
