A2. Level Curves
How can we represent the features of a multivariable function on a plane?
| Video |
Description |
| a. Level Curves of a Function (5:08) |
| (0:00) |
altitude contours of a terrain |
| (1:00) |
directions of steepest ascent |
| (1:30) |
hiking up and down along a trail |
| (2:05) |
orientation of a mountain’s level contours |
| (3:15) |
3-D surface of a function ƒ(x1,x2) |
| (3:37) |
projecting down to the (x1,x2) plane |
| (4:00) |
level curves of a function ƒ(x1,x2) |
| (4:10) |
level curves of a linear function |
| (4:25) |
level curves of the function ƒ(x1,x2) = x1•x2 |
| (4:45) |
level curves of a general nonlinear function |
|
| b. Slopes of Level Curves (5:54) |
| (0:00) |
level contours of a mountain vs. level curves of a function |
| (0:30) |
orientation of a mountain’s level contours vs. orientation of a function’s level curves |
| (2:35) |
slope of a given level curve |
| (4:05) |
two numerical examples |
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