The table below shows the temperature (in °F) t hours after midnight in Phoenix on March 15. The table shows values of this function recorded every two hours.

Question

Estimate the value of T′(10). Give units in your answer.
What is the meaning of T′(10)?

t 0 2 4 6 8 10 12 14

T 73 73 70 68 73 80 86 89

Answer 1

My first estimate of T'(10) would be the average change from t=8 to t=12:

(T(12)-T(8))/(12-8) = (86-73)/4 = 3.25

Using a forward estimate from t=10, it might be

(T(12)-T(10))/(12-10) = (86-80)/2 = 3.0