In a certain chemical reaction, substance A combines with substance
B to form substance Y . At the start of the reaction, the
quantity of A present is a grams, and the quantity of
B present is b grams. Assume a<b and y\le a .
At time t
seconds after the start of the reaction, the quantity of Y
present is y grams. For certain types of reactions, the rate of
the reaction, in grams/sec, is given by
\hbox{Rate}=k(a-y)(b-y),
where k is a positive constant.

**1.**
Sketch a graph of the rate against

*Give your answer as a union of intervals, e.g.,*
**(-infinity,-a] U (a, 2b)**

**2.**
Use your graph to find the value of

You can earn partial credit on this problem.