Firstly, we need to calculate the value of the function at the endpoints of the interval.
Let's start with the lower endpoint, which is x₁=5.
We substitute x₁=5 into the function f(x), which gives:
f(x₁)=f(5)=2(5)³-3(5)+8=243.
Next, we calculate the function value at the other endpoint of the interval, which is x₂=7.
Substituting x₂=7 into the function gives:
f(x₂)=f(7)=2(7)³-3(7)+8=673.
The average rate of change of the function f on the interval [x₁, x₂]=[5,7] is defined as the difference in the function values at the endpoints of the interval divided by the difference in the x-values.
So, the average rate of the function f(x) over the interval [5,7] is:
(f(x₂)-f(x₁))/(x₂-x₁) = (673-243)/(7-5) = 215.
Therefore, the average rate of change in the function f(x)=2x³-3x+8 on the interval [5,7] is 215.