Calculating the Average Rate of Change of f(x) = 1 + 3cos(x) over the Interval [0, π]

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 a given interval, we need to calculate the difference in the function values at the two endpoints of the interval and divide it by the difference in the x-coordinates of the endpoints

To find the average rate of change of a function over a given interval, we need to calculate the difference in the function values at the two endpoints of the interval and divide it by the difference in the x-coordinates of the endpoints.

In this case, the function f(x) = 1 + 3cos(x) is defined on the interval [0, π]. Therefore, we need to evaluate the function at the endpoints of the interval and calculate the difference in the function values.

First, let’s find the value of f(0):

f(0) = 1 + 3cos(0)
= 1 + 3(1)
= 1 + 3
= 4

Next, let’s find the value of f(π):

f(π) = 1 + 3cos(π)
= 1 + 3(-1)
= 1 – 3
= -2

Now, we have the function values at the endpoints. The difference in function values is:

f(π) – f(0) = -2 – 4
= -6

The difference in x-coordinates is:

π – 0 = π

Finally, we can calculate the average rate of change:

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.

More Answers:

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