# Integral/Derivative Problem Solving Question

1. Apr 5, 2006

### tangents

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. Apr 5, 2006

### dav2008

Do you have any specific questions regarding the problem?

Are you stuck on one particular question?

3. Apr 5, 2006

### tangents

i dont get the whole thing

4. Apr 5, 2006

### tangents

bump.........

5. Apr 5, 2006

### Jeff Ford

What have you tried so far?

6. Apr 5, 2006

### 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

7. Apr 5, 2006

### Hootenanny

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

-Hoot

8. Apr 5, 2006

### tangents

yeah that's basically what i did to estimate the slope at 7 but -24 just doesnt seem right

9. Apr 5, 2006

### Hootenanny

Staff Emeritus
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

10. Apr 5, 2006

### tangents

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