Let f be continuous on the interval [0, 1] to r and such that f(0) = f(1). prove that there exists a point c in [0, 1 2 ] such that f(c) = f c + 1 2 . [hint: consider g(x) = f(x) − f x + 1 2 ] conclude that there are, at any time, antipodal points on the earth’s equator that have the same temperatur

Ascientist places 24 cells in a petri dish. she knows the cells grow at an exponential rate, doubling in number every hour. how long will it take (in hours) for there to be 1100 cells in the dish? time to 1100 cells: 5.51832530 hours how long will it take to reach 110 cells? time to 110 cells : 2.1963972 hours what is the average rate of change in the number of cells between 9 hours and 11 hours? average rate of change: cells per hour what is the instantaneous rate of change after 7 hours? instantaneous rate of change: cells per hour note: you can earn partial credit on this problem.