$(15$ points$)$: In a vertical curve, a level$-$grade line is to connect a down going grade of $7\%.$ The elevations of this grade line at station $0+000$ is the same as the elevation of the PVI and is equal to $930\mathrm{.}5m$ AMSL. The station of the PVI is $2+210\mathrm{.}57.$ Due to some infrastructure constructions it is required that the elevation of the curve at the PVT is $923\mathrm{.}57m.$

Required:

a$).($S points$)$: Draw the vertical curve and show all details and given information on it$.$

b$).(5$ points$)$: Design the vertical curve and specify its type

c$).(5$ points$)$: What are the stations and elevations of the highest and lowest points on the curve.