Rates of change

1. Aug 26, 2008

Brunll

1. The problem statement, all variables and given/known data
Temperature readings T (in degrees celcius) were recorded every hour starting at midnight on a day in april in Whitefish, Montana.The time x is measured in hours from midnight.The data are giving in the table at the left

x(h) T(°C)

0 6.5
1 6.1
2 5.6
3 4.9
4 4.2
5 4.0
6 4.0
7 4.8
8 6.1
9 8.3
10 10.0
11 12.1
12 14.3

2. Relevant equations

Estimate the instantaneous rate of change at noon.

3. The attempt at a solution
I tried to understand the solution but still dont get it.so could somebody help me?

3. The attempt at a solution

2. Aug 26, 2008

snipez90

With just that set of data, noon is an endpoint if you plot it. I mean you could find the average temperature change between 11 AM and noon but that would not be a great estimate. I'm not sure what kind of solution you're looking for here. The best way to estimate the instantaneous rate of change is to plot the graph, use a ruler to draw a tangent line, and try figuring out the slope, but with the data set you've given, this won't work out too well.

3. Aug 26, 2008

Brunll

Thanks!I'll try it.

4. Aug 26, 2008

symbolipoint

Brunll, you could use the set of points and graph to develop a function, F(x) = something, and perform differentiation on it, and find the value of the derivative at the point where x=12

5. Aug 27, 2008

kenewbie

That data do not easily map to a function.

I would go with the slope of the tangent.

k

6. Aug 27, 2008

Redbelly98

Staff Emeritus
I think the 1st method mentioned here is more accurate than the 2nd method.

7. Aug 27, 2008

granpa

first convert the data to change in temperature per hour.

next to that make a chart of change in change in temperature per hour.