The Car Trip
  1. Draw a careful graph taking up at least a third of an 8.5x11 sheet of paper, of a continuous function d(t) which is always positive and which satisfies d(0)=0

  2. Interpret your graph as the plot of your car trip, with the independent variable t for time, and d(t) the distance from your point of origin.

  3. Compare the slope of the tangent line to the speedometer of the car in your mind's eye.

    The group with either (a) the most air-tight argument that these two numbers (the display on your speedometer, versus the slope of the tangent line to the graph of the function d(t) which represents the trip) must always be equal at corresponding points in time (explain your correspondence), or else, (b) with the best argument or example as to why they need not always be equal for all possible graphs of trips, carries the day.








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