Every second counts You must get from a point P on the

Chapter 4, Problem 77

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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). If you can swim at a speed of 2 m>s and run at a speed of 4 m>s, at what point along the shore, x meters from Q, should you stop running and start swimming if you want to reach the swimmer in the minimum time? 50 m swim run Q x 50 _ x P 50 m 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 10, 502. c. Evaluate T at the critical point and the endpoints 1x = 0 and x = 502 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.