Chapter 3.4, Problem 41E

Market Index Joe Downs runs a small investment company from his basement. Every week, he publishes a report on the success of his investments, including the progress of the Joe Downs Index. At the end of one particularly memorable week, he reported that the index for that week had the value $I\left(t\right)=1,000+1,500t-800t^2+100t^3$

points, where t represents the number of business days into the week; t ranges from 0 at the beginning of the week to 5 at the end of the week. The graph of I is shown below:

I(Joe Down Index)

On average, how fast and in which direction was the index changing over the first two business days (the interval $\left[0,2\right]$

)?[HINT: See Example 3.]