The function f is given by f(x)=1+3cosx. What is the average rate of change of f over the interval [0,π] ?
To find the average rate of change of a function over an interval, we need to determine the difference in function values at the endpoints of the interval and divide it by the difference in the input values (or x-values) at the endpoints
To find the average rate of change of a function over an interval, we need to determine the difference in function values at the endpoints of the interval and divide it by the difference in the input values (or x-values) at the endpoints.
Given the function f(x) = 1 + 3cos(x), we are interested in finding the average rate of change of f over the interval [0, π].
Let’s find the value of f at the endpoints of the interval:
f(0) = 1 + 3cos(0) = 1 + 3(1) = 1 + 3 = 4
f(π) = 1 + 3cos(π) = 1 + 3(-1) = 1 – 3 = -2
Now, let’s find the difference in function values at the endpoints:
f(π) – f(0) = -2 – 4 = -6
Next, let’s find the difference in input values (or x-values) at the endpoints:
π – 0 = π
Finally, we can calculate the average rate of change of f over the interval [0, π]:
Average rate of change = (f(π) – f(0)) / (π – 0) = -6 / π
Therefore, the average rate of change of f over the interval [0, π] is -6 / π.
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