In a certain chemical reaction, substance [math] combines with substance [math] to form substance [math]. At the start of the reaction, the quantity of [math] present is [math] grams, and the quantity of [math] present is [math] grams. Assume [math] and [math]. At time [math] seconds after the start of the reaction, the quantity of [math] present is [math] grams. For certain types of reactions, the rate of the reaction, in grams/sec, is given by [math] where [math] is a positive constant.

1. Sketch a graph of the rate against [math]. For what values of [math] is the rate nonnegative?
Give your answer as a union of intervals, e.g., (-infinity,-a] U (a, 2b)
[math]

2. Use your graph to find the value of [math] at which the rate of the reaction is fastest.
[math]