A small island is 3 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 12 miles down the shore from P in the least time? Let be the distance between point P and where the boat lands on the lakeshore. Hint: time is distance divided by speed.
(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 units.
(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 ?
I got the first one, which is (sqrt(x^2+9))/2+(12-x)/3
also how do I derive that? do I used chain rule for the first function?