I am given a table that shows the temperature of the water and the days, which looks like this:
t(days) W(t) (in Celcius)
0 20
3 31
6 28
9 24
12 22
15 21
the temperature of the water in a pond is a differentiable function W of time t. The table above shows the water temperature recorded every 3 days over a 15-day period.
Use data from the table to find an approximation for W'(12). Show the computations that lead to your answer.
I am not sure about what to do. I've tried graphing it, but I didn't know what to do from there. What other methods can I use?
w'= deltaW/delta time= (21-24)/6 in degreesC per day.
If you graph it, approximate the tangent between day 9 and day 15.
so the final answer would be 1/2degrees celcius at time=12?
I meant -1/2.