A lifeguard is at point A of a circular pool with diameter 40 m. He must reach someone who is drowning on the exact opposite side of the pool, at position C. The lifeguard swims with a speed v = 3 m/s from point A to point B, and then runs around the pool from point B to point C at speed w = 9 m/s.

How do we know that the functionT(x) has a maximum and minimum?

What restrictions are there on what the domain ofTcan be in this scenario?

Elaborate on why we must evaluateT(0) andT(6).