Table of Contents
- is used to encode infinitesimal changes
- used to act as a placegolder value
- divide wrt time to get rate of change CHAIN RULE
Chain Rule with More Variables
Let when then,
Note: (tangent to the level surface at any given point)
Direction of is the direction of fastest increase of
Goal: minima/maximize a multi-variable function () where are not independent and .
These can be obtained on combining the given restraints with the following.
Basic idea: to find where the level curves of and are tangent to each other ().
Note: Take care that the point is indeed a maxima or minima as required and not just a saddle point (second derivative test won't be applicable so be vigilant).