# 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:
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.