Please solve question 4, 5 and 6 in details and fully explanation.

Question 6.4 (20 minutes) Find the local maxima and minima and inflection points of the function f (20) = 1202 - 32 + 21. Question 6.5 (20 minutes) a) Find the absolute maximum of the function y = x1/x on (0, co) b) Based on the previous part, determine for what values a > 0, a # 1, equation logax = x has a solution (you don't need to actually solve for x). Question 6.6 (20 minutes) Two runners run 400 meters starting from the same position at the same time. If both of them run the distance in 50 sec, then argue using the mean value theorem that a) There was at least one moment when the first athlete's speed was exactly 8 meters per second. b) There was at least one moment when the second athlete's speed was exactly 8 meters per second. c) There was at least one moment when both of them had the same speed