The temperature, in degrees Celsius ("C) of the water in a pond is a differential function of time "". The table below shows the water temperature as recorded on various days for a 15-day period. (days) w() (C) 0 2 6 10 13. 15 27 31 35 36 31 24 a) Use the data from the table to find an approximation for w'(8). Show the computations that lead to your answer. Using correct units, interpret the meaning of w'(8) in the context of the problem. b) Do the data in the table support the conclusion that at some time during the 15 day period w'(t) 0? If so, within what time interval? Give a reason to support your answer. c) Do the data in your table support the conclusion that the water temperature at some point in the 15 day period is equal to 25C? If so, within what smallest time interval? Justify your conclusion. d) Use Trapezoidal sums with five subintervals and values from the table to approximate 15 Sw(t)dt.