We are working with a function z = f(x,y) whose rules we don't know. But we do have a table of values for d/dx f(x,y).
1) GIven that f(3,12) = 1, use the tangent line approximation to estimate the value of f(3.5, 12)
| x/y |
12 |
13 |
14 |
15 |
16 |
| 3 |
0.278 |
0.204 |
0.156 |
0.123 |
0.1 |
| 4 |
0.208 |
0.153 |
0.117 |
0.0926 |
0.075 |
| 5 |
0.167 |
0.122 |
0.0938 |
0.0741 |
0.06 |
| 6 |
0.139 |
0.102 |
0.0781 |
0.0617 |
0.05 |
| 7 |
0.119 |
0.0875 |
0.067 |
0.0529 |
0.0429 |