Mathematical formulas

Differential Calculus

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1Notation, functions and domains
2Limits
3Continuity
4Derivative and geometric interpretation
5Differentiation rules
6Higher-order derivatives
7Mean value theorem
8Function analysis
9Optimization
10Linear approximations and differentials
11Taylor series (introduction)
12L'Hôpital and indeterminate limits
13Implicit and related functions
14Related rates
15Graphs and asymptotic behavior
16Guide to differentiate and analyze
AAppendix A: extended derivative table

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Differential Calculus
Linear approximation
Formula

10.2. Linear approximation

Formula

In 10.2. Linear approximation

Formula

L(x)=f(a)+f'(a)(x-a)

Tags

Linear approximation
Differential calculus
Derivative
Differential
Derivative formula
Taylor

Detail

Degree-1 Taylor polynomial (linear approximation at

a

).

Explore the idea

Explore the idea

Variables

$x$ Independent variable
$a$ Point or real constant
$f$ Function
$f'$ Derivative of $f$
$L$ Limit value

Related topics

Taylor series

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