Question: A meteorologist sketched the path of the jet stream on a map of the northern U.S. and southern Canada on which all latitudes were parallel and all longitudes were parallel and equally spaced. A computer analysis showed this path to be given by:

\[y=\left( 6.0{{e}^{-0.020x}} \right)\left( \sin 0.20x \right)\text{ where }0\le x\le 60\]

\[\text{The origin is 125}\text{.}{{\text{0}}^{\circ }}W,{{45.0}^{\circ }}N\text{ and the point (60,0) is 65}\text{.}{{\text{0}}^{\circ }}W,{{45.0}^{\circ }}N\].

Find the locations of the maximum and minimum latitudes of the jet stream between \[{{65}^{\circ }}W\text{ and 12}{{\text{5}}^{\circ }}W\] for that day.