The function f is given by f(x)=1+3cosx. What is the average rate of change of f over the interval [0,π] ?
-6/πThe difference quotient [f(π)−f(0)]/(π−0) is the average rate of change of ff over the interval [0,π][0,π].
To find the average rate of change of the function f(x) over [0,π], we need to use the formula:
Average rate of change of f(x) = (f(π) – f(0)) / (π – 0)
First, let’s find f(π) and f(0):
f(π) = 1 + 3cos(π) = 1 – 3 = -2
f(0) = 1 + 3cos(0) = 1 + 3 = 4
Now, we substitute these values into the formula to get:
Average rate of change of f(x) = (-2 – 4) / π = -6/π
Therefore, the average rate of change of f over the interval [0,π] is -6/π.
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