Not sure how to approach this:
Help?
11.
A small island is 4 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 9 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.
(A) Enter a function T(x) that describes the total amount of time the trip takes as a function of the distance x.
(B) What is the distance x = c that minimizes the travel time?
(C) What is the least travel time?
(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)?
Any help would be appreciated. I am not sure how to approach this.
Thanks
Help?
11.
A small island is 4 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 9 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.
(A) Enter a function T(x) that describes the total amount of time the trip takes as a function of the distance x.
(B) What is the distance x = c that minimizes the travel time?
(C) What is the least travel time?
(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)?
Any help would be appreciated. I am not sure how to approach this.
Thanks