I need help with part 2, part 1 is there for context.

Question:

Part I

An island is 2mi due north of its closest point along a straight shoreline. A visitor is staying at a cabin on the shore that is 6mi west of that point. The visitor is planning to go from the cabin to the island. Suppose the visitor runs at a rate of 8mph and swims at a rate of 3mph. How far should the visitor run before swimming to minimize the time it takes to reach the island?

Part II

Answer the following questions in detail that reference Example 4.34 above:

1. How do we know that the functionT(x) has a maximum and minimum?
2. What restrictions are there on what the domain ofTcan be in this scenario?
3. Elaborate, on why we must evaluateT(0) andT(6).

Reference: https://openstax.org/books/calculus-volume-1/pages/4-7-applied-optimization-problems