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≤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

Question

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∈

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

Thank you so much. I am so clueless.