Applications of multivariable derivatives

Tangent planes and local linearization
Quadratic approximations
Optimizing multivariable functions
Optimizing multivariable functions (articles)
Lagrange multipliers and constrained optimization
Constrained optimization (articles)
About this unit
The tools of partial derivatives, the gradient, etc. can be used to optimize and approximate multivariable functions. These are very useful in practice, and to a large extent this is why people study multivariable calculus.