- #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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