Asmall 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 3 miles per hour and can walk 4 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 x be the distance between point p and where the boat lands on the lake shore.
(a) enter a function t(x) that describes the total amount of time the trip takes as a function of the distance x.
t(x) =
(b) what is the distance x=c that minimizes the travel time? note: the answer to this problem requires that you enter the correct units.
c = .
(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 t′(c)=0 and t′′(c)> 0, then t has a local minimum at c. what is t′′(c)?
t′′(c) =