Question

Let f be defined as f(x) = x⁴ - 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 1

The average rate of change of the function f(x) = x⁴ - 2x on the closed interval [0, 4] is 62.

Step-by-step explanation:

The average rate of change of a function on a closed interval is determined by finding the difference in the function values at the two endpoints of the interval, and then dividing this difference by the length of the interval. In this case, the function is f(x) = x⁴ - 2x, and the closed interval is [0, 4].

So, f(4) - f(0) = (4⁴ - 2(4)) - (0⁴ - 2(0)) = 256 - 8 - 0 + 0 = 248. The length of the interval is 4 - 0 = 4. Therefore, the average rate of change of the function f on the interval [0, 4] is 248/4 = 62. Answer choice c) 62 is the correct answer.