Every second counts You must get from a point P on the straight
shore of a lake to a stranded swimmer who is 50 m from a point
Q on the shore that is 50 m from you (see figure). Assuming that
you can swim at a speed of 2 m/s and run at a speed of 4 m/s,
the goal of this exercise is to determine the point along the shore,
x meters from Q, where you should stop running and start swimming
to reach the swimmer in the minimum time.
a. Find the function T that gives the travel time as a function of x,
where 0 ≤ x ≤ 50.
b. Find the critical point of T on (0, 50).
c. Evaluate T at the critical point and the endpoints (x = 0 and
x = 50) to verify that the critical point corresponds to an absolute
minimum. What is the minimum travel time?
d. Graph the function T to check your work.
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