MATH 2301-102 Fall 2018 Calculus I Recitation 8 Week 12

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

  1. 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.
  2. A particle moves in a straight line with velocity (in feet per second) given in the graph: velocity function
    1. Determine the position function \(s(t)\) at \(t=1\), 2, 3, 4, 5, 6, and 7, assuming \(s(0)=0\).
    2. Sketch a graph of \(s(t)\). Make sure your graph shows where \(s\) is concave up and where it is concave down.
  3. 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. water cone

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