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Answer :
The average rate of change of the function f on the interval [0, 4] is calculated using the formula (f(b) - f(a)) / (b - a), leading to a result of 62.
The student is asking to find the average rate of change of the function f(x) = x4 - 2x on the closed interval [0, 4]. To calculate this, we use the formula for the average rate of change over an interval [a, b], which is (f(b) - f(a)) / (b - a).
Firstly, we find the values of the function at the endpoints of the interval:
- f(0) = 04 - 2(0) = 0
- f(4) = 44 - 2(4) = 256 - 8 = 248
Next, we apply the values to the formula:
Average rate of change = (f(4) - f(0)) / (4 - 0) = (248 - 0) / 4 = 248 / 4 = 62.
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