A mouse named Minnie can run back and forth along a straight path in her cage for 24 hours. On one day, her position is modeled by S = 5 cos (t) + 2, where t is hours 12 since midnight, and S is her position in metres relative to the centre of the cage. a) Calculate Minnie's position at midnight. b) At what rate is her position changing at 2:00 p.m.? c) At what time, within 24 hours is her speed the fastest?

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