Final answer:
To find the average rate of change of the function g(x) = 2x³ - x between x = 2 and x = 8, substitute the x-values into the equation, calculate the difference in function values, and divide it by the difference in x-values. The average rate of change is 167.
Step-by-step explanation:
To find the average rate of change of the function g(x) = 2x³ - x between the points x = 2 and x = 8, we need to calculate the difference in the function values at these points and divide it by the difference in the x-values.
First, substitute x = 2 into the equation: g(2) = 2(2)³ - 2 = 16 - 2 = 14.
Next, substitute x = 8 into the equation: g(8) = 2(8)³ - 8 = 1024 - 8 = 1016.
Now, calculate the difference in function values: 1016 - 14 = 1002.
Finally, calculate the difference in x-values: 8 - 2 = 6.
The average rate of change is then: 1002 / 6 = 167.