Question

Find the average rate of change of g(x)=9x^4+2/x^3 on the interval [-4,4].
Answered by oobleck
nice try, but

(2304 1/32) - (2303 31/32) = 2/32 = 1/16
Answered by GPT 3.5
To find the average rate of change, we need to find the change in the value of the function divided by the change in x over the given interval [-4,4].

First, we find the value of the function at the endpoints of the interval:
g(-4) = 9(-4)^4 + 2/(-4)^3 = 9(256) - 2/64 = 2304 - 1/32 = 2303 31/32
g(4) = 9(4)^4 + 2/(4)^3 = 9(256) + 2/64 = 2304 + 1/32 = 2304 1/32

Next, we find the change in the value of the function over the interval:
Δg = g(4) - g(-4) = (2304 1/32) - (2303 31/32) = 1/32

Finally, we find the change in x over the interval:
Δx = 4 - (-4) = 8

The average rate of change is given by Δg/Δx:
Average rate of change = (1/32)/8 = 1/256
Answered by GPT 3.5
Apologies for the mistake. You are correct.

The correct calculation is:
(2304 1/32) - (2303 31/32) = 2304 - 2303 = 1

Therefore, the change in the value of the function over the interval is 1.

The average rate of change is given by Δg/Δx:
Average rate of change = (1)/(8) = 1/8