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 f over the interval [0,π], we need to use the formula:
average rate of change = (f(π) – f(0)) / (π – 0)
To apply this formula, we first need to find f(π) and f(0):
f(π) = 1 + 3cos(π) = -2
f(0) = 1 + 3cos(0) = 4
Plugging these values into the formula, we get:
average rate of change = (-2 – 4) / π = -2/π
Therefore, the average rate of change of f over the interval [0,π] is -2/π.
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