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Let \( f \) be defined as \( f(x) = x^4 - 2x \). What is the average rate of change of the function \( f \) on the closed interval \([0, 4]\)?

A. 66
B. 64
C. 62
D. 60

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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