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
Critical points and extrema
Formula

8.3. Critical points and extrema

Formula

In 8.3. Critical points and extrema

Formula

f'(c)=0\ \text{or}\ f'(c)\text{ does not exist} \Rightarrow c\text{ is a critical point}

Tags

Analysis
Critical points and extrema
Differential calculus
Derivative
domain restriction

Detail

c

belongs to the domain of

f

and to the interior of the interval under consideration.

Variables

$c$ Intermediate point (MVT, Rolle)
$f$ Function
$f'$ Derivative of $f$

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