Question 1141836
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 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.
the distance rowed is the hypotenuse of 3 & x, and the distance walked is 10-x
time = dist/speed
T(x) = {{{(sqrt(3^2+x^2)/2)}}} + {{{((10-x)/3)}}}
(B) What is the distance x = c that minimizes the travel time?
{{{ graph( 300, 200, -3, 8, -2, 8, ((sqrt(3^2+x^2)/2)+((10-x)/3)), 4.45) ) }}}
Minimum x = 2.75 mi, travel time: 4.45 hrs (green)
 Note:
 The answer to this problem requires that you enter the correct units.
c = 2.75 mi
(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 : 4.45 hrs
(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) =
Actually, I don't recall this.