I need help on this question for calculus please!

Question

t 0 2 4 6 8 10 12 14

T 73 73 70 68 73 80 86 89

This table is showing the temperature (t), in Fahrenheit, in hours on March 15 midnight in Phoenix. These values are recorded every two hours. Estimate the value of T'(6), and please include the units with the answer. Furthermore, what is the meaning of T'(6)?

Answer 1

T'(t) is the slope of the temperature function T(t), the rate of change of temperature vs. time in degrees per hour, dT/dt. T'(6) is the rate of change 6 hours after midnight. Since T(6) is the minimum value on the interval, T'(6) = 0.