What is the Instantaneous Rate of Change at Noon?

[Brunll]

Homework Statement

Temperature readings T (in degrees celsius) 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

Homework Equations

Estimate the instantaneous rate of change at noon.

The Attempt at a Solution

I tried to understand the solution but still don't get it.so could somebody help me?

The Attempt at a Solution

 

[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.

 

[Brunll]

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.

Thanks!I'll try it.

 

[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

 

[kenewbie]

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

That data do not easily map to a function.

I would go with the slope of the tangent.

k

 

[Redbelly98]

... you could find the average temperature change between 11 AM and noon but that would not be a great estimate.

... 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.

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

 

[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.