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Rates of change

  1. Aug 26, 2008 #1
    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. jcsd
  3. Aug 26, 2008 #2
    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.
  4. Aug 26, 2008 #3
    Thanks!I'll try it.
  5. Aug 26, 2008 #4


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    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
  6. Aug 27, 2008 #5
    That data do not easily map to a function.

    I would go with the slope of the tangent.

  7. Aug 27, 2008 #6


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    I think the 1st method mentioned here is more accurate than the 2nd method.
  8. Aug 27, 2008 #7
    first convert the data to change in temperature per hour.

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