Find the average rate of change of g(x)=2x^3+7/x^2 on the interval [-4,3]
To find the average rate of change of a function g(x) on an interval [a, b], we can use the formula:
Average rate of change = [g(b) - g(a)] / (b - a)
In this case, g(x) = 2x^3 + 7/x^2 and the interval is [-4, 3].
First, we find g(3):
g(3) = 2(3)^3 + 7/(3)^2
g(3) = 54 + 7/9
g(3) = 54 + 0.7777777778
g(3) = 54.7777777778
Next, we find g(-4):
g(-4) = 2(-4)^3 + 7/(-4)^2
g(-4) = 2(-64) + 7/16
g(-4) = -128 + 0.4375
g(-4) = -127.5625
Now, we calculate the average rate of change:
Average rate of change = [g(3) - g(-4)] / (3 - (-4))
Average rate of change = [54.7777777778 - (-127.5625)] / 7
Average rate of change = 182.3402777778 / 7
Average rate of change ≈ 26.05
Therefore, the average rate of change of g(x)=2x^3+7/x^2 on the interval [-4,3] is approximately 26.05.