Land Lake X 4 miles 1 mile An athlete is planning for the "Land and Lake Race," the path of which is shown in the figure above. The contestants will start at the dot, run up to 4 miles along the beach, enter the water at any time, and swim to the island. The athlete estimates that they can run along the beach at a constant rate of 8 miles per hour and swim at a constant rate of 2 miles per hour. Let 7 be a function that represents the time to complete the race, where x is the distance in miles that the athlete runs and T ( ) is measured in hours. Which of the following methods best explains how to determine the minimum time, in hours, the athlete should run along the beach and then swim to the island?A Let T (a) = 8x + 21 12 + (4 - a) . Solve T' (x) = 0 and find the values of a where T (a) changes sign from negative to positive. Evaluate T for those values of a to determine the minimum time. V12 + ( 4-20)? B Let T (ac) = 2 . Solve T' (a) = 0 and find the values of a where T (x) changes sign from negative to positive. Evaluate T for those values of a to determine the minimum time. Let T (ac) = + V12+22 C 2 Solve T' (x) = 0 and find the values of a where T (a ) changes sign from negative to positive. Evaluate T for those values of x to determine the minimum time. V ( 4 -20) D Let T (ac) = 2+ . Solve T' (x) = 0 and find the values of a where T (a ) changes sign from negative to positive. 2 Evaluate T for those values of x to determine the minimum time. <