Integral/Derivative Problem Solving Question

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  • #1
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Code:
----------------------------------------------
| 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
 
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Answers and Replies

  • #2
dav2008
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Do you have any specific questions regarding the problem?

Are you stuck on one particular question?
 
  • #3
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i dont get the whole thing
 
  • #4
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bump.........
 
  • #5
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What have you tried so far?
 
  • #6
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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
 
  • #7
Hootenanny
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This is interesting becuase I've just plotted your results and found that they are pratically linear :confused:

-Hoot:smile:
 
  • #8
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yeah that's basically what i did to estimate the slope at 7 but -24 just doesnt seem right
 
  • #9
Hootenanny
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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.

-Hoot:confused:
 
  • #10
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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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