Question

Find the average rate of change of g(x) = 2x4 + 4/x^2
on the interval (-1,4]

Answer 1

The average rate of change of the function g(x) = 2x^4 + 4/x^2 on the interval (-1, 4] is found by computing the function values at x = -1 and x = 4, then calculating the difference and dividing by the interval length, yielding an average rate of change of 101.25.

Step-by-step explanation:

The average rate of change of a function g(x) over an interval [a, b] is defined as the change in the function values divided by the change in x, or (g(b) - g(a)) / (b - a). For the given function g(x) = 2x4 + 4/x2 over the interval (-1, 4], we calculate g(-1) and g(4). Then, we apply the formula for average rate of change.

1. Calculate g(-1) = 2(-1)4 + 4/(-1)2 = 2 + 4 = 6.
2. Calculate g(4) = 2(4)4 + 4/(4)2 = 2(256) + 4/16 = 512 + 0.25 = 512.25.
3. Find the average rate of change: ((512.25 - 6)) / (4 - (-1)) = 506.25 / 5 = 101.25.

The average rate of change of g(x) on the interval (-1, 4] is 101.25.