1. (10 pts) State the meaning of constant speed that we have publicly agreed to use.

An object is moving at a constant speed (distance with respect to time) if and only if

2. (10 pts) State the meaning of average speed that we have publicly agreed to use.

3. (10 pts) Extend the above meaning of average speed to average rate of change of one quantity with respect to another.

4. (12 pts) A spherical container is being filled. The supervisor records the amount of water in the tank and the water's depth in the tank at two moments in time.
At 2.72 feet there were 99.35 gallons of water in the tank.
At 4.35 feet there were 175.72 gallons of water in the tank.
What was the average rate of change of volume with respect to height over this interval of height? Explain what this number means.

5. (10 pts) What role does the "Fictitious Object" play in making the idea of average rate of change sensible?

6. (18 pts) Here is an "average rate" function. Please circle various parts of it and explain what they mean.

7. (20 pts) Draft a GC document (points, vectors, and functions) that will produce something like this display. Your document should work with any function a user enters and it should by dynamic in that the secant can move.