- During a chemical reaction, a compound is being made from two other substances.
At time \(t\) hours after the start of the reaction, \(x \mathrm {~g}\) of the compound has been produced. Assuming that \(x = 0\) initially, and that
$$\frac { \mathrm { d } x } { \mathrm {~d} t } = 2 ( x - 6 ) ( x - 3 )$$
- show that it takes approximately 7 minutes to produce 2 g of the compound.
- Explain why it is not possible to produce 3 g of the compound.