A small island is 2 miles from the nearest point P on the straight
shoreline of a large lake. If a woman on the island can row a boat
2 miles per hour and can walk 3 miles per hour, where should
the boat be landed in order to arrive at a town 10 miles down the
shore from P in the least time? Let be the distance between
point P and where the boat lands on the lake shore.
(A) Enter a function that describes the total amount of
time the trip takes as a function of the distance .
(B) What is the distance that minimizes the travel time?
Note: The answer to this problem requires that you enter the correct
(C) What is the least travel time? Note: The answer to this problem
requires that you enter the correct units
The least travel time is
(D) Recall that the second derivative test says that if and , then has a local minimum at
What is ?
You can earn partial credit on this problem.