Lagrange Multipliers
Optimised Extremum
The method of Lagrange multipliers allows us to maximize or minimize functions with the constraint
that we only consider points on a certain surface.
Using the above key point, we can conclude that the gradient of and should be parallel at the point of extremum. Since if they are not parallel then there will be a component of on and the gradient will increase in that direction in order to maximise .
Key Point:
The gradient of a function is in the direction of steepest increase of the function and is orthogonal to the contour lines.Using the above key point, we can conclude that the gradient of and should be parallel at the point of extremum. Since if they are not parallel then there will be a component of on and the gradient will increase in that direction in order to maximise .