Mathematical formulas

Differential Calculus

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Sections

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
Theorems on continuous functions
Formula

3.3. Theorems on continuous functions

Formula

In 3.3. Theorems on continuous functions

Formula

f\text{ is continuous at }[a,b] \Rightarrow f\text{ attains absolute maximum and minimum on }[a,b]

Tags

Differential calculus
Continuity
Theorems on continuous functions

Detail

Extreme value theorem.

Variables

$a$ Point or real constant
$b$ Interval endpoint or constant
$f$ Function
$y$ Dependent variable

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$f,g\text{ are continuous at }a \Rightarrow f\pm g,\ fg,\ \frac{f}{g}\text{ are continuous at }a\ (g(a)\neq0)$
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$f\text{ is continuous at }[a,b],\ f(a)\neq f(b) \Rightarrow \forall k\in(\min\{f(a),f(b)\},\max\{f(a),f(b)\})\ \exists c\in(a,b): f(c)=k$
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