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Homework Help: Integral/Derivative Problem Solving Question

  1. Apr 5, 2006 #1
    Code (Text):
    | Distance x in cm |   0 |  1 |  5 |  6 |  8 |
    | Temp t(x) in °C  | 100 | 93 | 70 | 62 | 55 |
    Metal wire is 8 cm. and heated at one end. distance x is how far from the heated end you are. The function ti s decreasing and twice differentiable.
    a) estimate t'(7)
    b) write an integral expression of T(x) for avg temp of wire. estimate avg temp of wire using trapezoidal sum with 4 subintervals indicated by data
    c) Find int up limit 8 lower limit 0. explain the meaning of this in the context of the problem
    d) Is that data consistent with teh assertion that T''(x)>0 for every x from 0 to 8. explain
    Last edited: Apr 5, 2006
  2. jcsd
  3. Apr 5, 2006 #2


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    Do you have any specific questions regarding the problem?

    Are you stuck on one particular question?
  4. Apr 5, 2006 #3
    i dont get the whole thing
  5. Apr 5, 2006 #4
  6. Apr 5, 2006 #5
    What have you tried so far?
  7. Apr 5, 2006 #6
    for part a, I tried to get the slope from 6-8, which is the derivative and plug in 7 but i am not sure if that;s correct because it came out to be -24.5
  8. Apr 5, 2006 #7


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    This is interesting becuase I've just plotted your results and found that they are pratically linear :confused:

  9. Apr 5, 2006 #8
    yeah that's basically what i did to estimate the slope at 7 but -24 just doesnt seem right
  10. Apr 5, 2006 #9


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    There's something a miss though, if your relationship is linear, then this will lead to a constant t'(x). Anyway, my value for t'(x) is -5.761. I can't see through this calculus though, with a linear expression.

  11. Apr 5, 2006 #10
    Will it work if i try to find the slope of teh secant line to get the slope of the tangent line?
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