Chapter 4.2, Problem 11E

To determine

To explain : The reason why trucker was cited for speeding.

Answer to Problem 11E

This implies that the trucker had to be travelling at least $79.5$ miles per hour—over the speed limit—at some point on the toll road.

Explanation of Solution

Given information:

The trucker handed in a ticket at a toll booth showing that in $2h$ she had covered $159\mathrm{mi}$ on the toll road with speed limit $65mph$ .

Explain:

According to the Mean Value Theorem, there must be a point on the function that equals that average when the average slope (or speed in this example) for the entire function is calculated. In two hours, the trucker travelled $159$ miles. The average speed is $79.5$ miles per hour.

This implies that the trucker had to be travelling at least $79.5$ miles per hour—over the speed limit—at some point on the toll road.