See the coversheet for instructions and the point value of each problem.

- Let \(f\) be a continuous function with \(f(0)=3\), \(f(2)=6\), \(f'(x)=0\) for \(0 \lt x \lt 1\), and \(f'(x) \lt 2\) for \(1 \lt x \lt 2\). Sketch such a function or explain why it is impossible.
- A particle moves in a straight line with velocity (in feet per second) given in the graph:
- Determine the position function \(s(t)\) at \(t=1\), 2, 3, 4, 5, 6, and 7, assuming \(s(0)=0\).
- Sketch a graph of \(s(t)\). Make sure your graph shows where \(s\) is concave up and where it is concave down.

- A cone-shaped drinking cup is made from a circular piece of paper of radius \(5\,\mathrm{in}\) by cutting out a sector and joining the edges \(CA\) and \(CB\). Find the maximum capacity of such a cup.

Last modified: Wed Nov 7 18:19:27 UTC 2018