Answer:
79.78125
Explanation:
The average rate of change (m) on an interval [a, b] is found as ...
m = (g(b) -g(a))/(b -a)
Here, that is ...
m = (g(4) -g(-2))/(4 -(-2))
g(-2) = 2(-2)^4 +7/(-2)^2 = 32+7/4 = 33.75
g(4) = 2(4^4) +7/(4^2) = 512 +7/16 = 512.4375
Then ...
m = (512.4375 -33.75)/6 = 478.6875/6 = 79.78125
The average rate of change of g(x) on [-2, 4] is 79.78125.
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The attached graph verifies the calculation and shows the line with that slope goes through the endpoints of the interval.