1. The position of an object moving along a line is given by the function s(t) = t^2-2t .

1. The position of an object moving along a line is given by the function s(t) = t^2-2t .
What is the average velocity over the interval [0, 2] ?
2. The position of an object moving along a line is s(t) = t^2-2t . Approximate the instantaneous velocity at the point t = 1
3. Consider the graph of y = x^3 . Find the slope of the secant line between the points
corresponding to x = -1 and x = 1.
4. Which of the following values is the best approximation to the slope of the line tangent to
the graph of y = x^3 and x = 0?
a. 0 b. 3 c. -2
5. What is the slope of the line tangent to the graph of f at (a, f(a)) ?

6. The function s(t) represents the position of an object at time t moving along a line.
Suppose s(3) = 161 and s(6) = 245 . Find the average velocity of the object over the interval
of me [3, 6] by hand, showing all work.

7. For the position function s(t) = −16t^2+110t :

a) Complete the following table with the appropriate average velocities (show work and
give up to 3 decimal places)
Time Interval    [0.99, 1]           [1, 1.01]
Average
Velocity
b) Make a conjecture about the value of the instantaneous velocity at t = 1. _______