Find the average rate of change of g(x)=2x^4 + 7/x^2 on the interval [-2,4]

  79.78125

Step-by-step 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.

_____

The attached graph verifies the calculation and shows the line with that slope goes through the endpoints of the interval.

answer: a.

step-by-step explanation: the answer is a. because, you need to converge the fractions to find a solution.