# Math

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.

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

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

posted by Steve

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