6. Two players on a basketball team share playing time. Mark's expected number of points scored is SM(x) = 30x – 5x² if he plays the fraction x e [0,1] of the game. John's expected number is S(x) =...

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Extracted text: 6. Two players on a basketball team share playing time. Mark's expected number of points scored is SM(x) = 30x – 5x² if he plays the fraction x e [0,1] of the game. John's expected number is S(x) = 25x – 5x points if he plays the fraction x of the game. (i) Suppose that Mark plays the entire game. How many points does he expect to score? How many points would John expect to score if he played the fraction x = A of the game? Find the average scoring rate, S(A)/A, as A approaches zero. (ii) What fraction of the time should Mark play in order to maximize the total points scored by Mark and John? Find the expected number of points scored by each player per unit time.