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 $y$. For what values of $y$ is the rate nonnegative?
Give your answer as a union of intervals, e.g., (-infinity,-a] U (a, 2b)
$y\in$

2. Use your graph to find the value of $y$ at which the rate of the reaction is fastest.
$y =$