# linear approximation

(1.5 hours to learn)

## Summary

A function is differentiable at a point x if it can be approximated by a linear function around x. The linear approximation can be computed in terms of the partial derivatives at x.

## Context

This concept has the prerequisites:

- partial derivatives (The linear approximation is computed from partial derivatives.)
- dot product (The linear approximation is given in terms of a dot product.)
- limits and continuity in R^n (Differentiability requires continuous partial derivatives.)

## Core resources (read/watch one of the following)

## -Paid-

→ Multivariable Calculus

An introductory multivariable calculus textbook.

Location:
Section 13.6, "Increments and linear approximation," pages 889-895

→ Multivariable Mathematics

A textbook on linear algebra and multivariable calculus with proofs.

Location:
Section 3.2, "Differentiability," pages 87-95

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ MIT Open Courseware: Multivariable Caclulus (2010)

Video lectures for MIT's introductory multivariable calculus class.

Location:
Lecture 27, "Approximation formula"

## See also

-No Additional Notes-