14.6 - Multivariable Chain Rule
Theorem
Let
be a differentiable function of n variables.
Supposeare differentiable functions of m independent variables
Then for
Mnemonic
Ex:
Recall
14.7 Optimization
Local Extreme Values
A function
has a local extremum at if there exists a neighborhood such that
- local maximum
- local minimum
Critical Points
A point
in the domain of is called a critical point if
does not exist or does not exist
Theorem
If
has a local min/max at then is a critical point of