![]() |
|||||
|
|||||
![]() |
|||||
![]() |
![]() |
In our example we seek the maximum of F: F = xy, subject to the condition G = ax2 + by2 -1 = 0. The gradient of F is (y, x) and the gradient of G is (2ax, 2by). The determinant of the matrix whose columns are these vectors is 2by2-2ax2, so that our extremum condition, that this determinant is 0, becomes by2 = ax2. If we apply the condition G = 0, we see that each of by2 and ax2 must be 1/2. Since there are two x values that obey this condition (namely,
plus or minus the square root of |
![]() |