Project: Sparse Data
Section 3.3 - 10 points
Due:
Assume that f(x) and g(x) are differentiable functions about which we know very little. In fact, assume that all we know about these functions is the following table of data:
|
x |
f(x) |
f ‘(x) |
g(x) |
g ‘ (x) |
|
-2 |
3 |
1 |
-5 |
8 |
|
-1 |
-9 |
7 |
4 |
1 |
|
0 |
5 |
9 |
9 |
-3 |
|
1 |
3 |
-3 |
2 |
6 |
|
2 |
-5 |
3 |
7 |
? |
This isn’t a lot of information. For example, we can’t compute f ‘ (3) with any degree of accuracy. But we are still able to figure some things out, using the rules of differentiation.
1. Let 
2. Let 
3. Let 
4. Let 
5. Let 