Integral/Derivative Problem Solving Question

[tangents]

----------------------------------------------
| 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 the assertion that T''(x)>0 for every x from 0 to 8. explain

 

[dav2008]

Do you have any specific questions regarding the problem?

Are you stuck on one particular question?

 

[tangents]

i don't get the whole thing

 

[tangents]

bump...

 

[Jeff Ford]

What have you tried so far?

 

[tangents]

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

 

[Hootenanny]

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

-Hoot

 

[tangents]

yeah that's basically what i did to estimate the slope at 7 but -24 just doesn't seem right

 

[Hootenanny]

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

 

[tangents]

Will it work if i try to find the slope of the secant line to get the slope of the tangent line?