A small island is 5 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where should the boat be landed in order to arrive at a town 11 miles down the shore from P in the least time? Let x be the distance between point P and where the boat lands on the lakeshore. Hint: time is distance divided by speed. Recall that the second derivative test says that if T′(c)=0 and T″(c)0, then T has a local minimum at c. What is T″(c)?

Question

A small island is 5 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where should the boat be landed in order to arrive at a town 11 miles down the shore from P in the least time? Let x be the distance between point P and where the boat lands on the lakeshore. Hint: time is distance divided by speed. Recall that the second derivative test says that if T′(c)=0 and T″(c)>0, then T has a local minimum at c. What is T″(c)?