Mathematical formulas

Differential Calculus

Subjects Home Search Guide

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

Search formulas…

Language

Loading formula…

Mathematical formulas · API-served content · Guide

About Reviews Contact

Home
Differential Calculus
Definition
Formula

3.1. Definition

Formula

In 3.1. Definition

Formula

f\text{ is continuous at }[a,b] \Rightarrow f\text{ attains every value between }f(a)\text{ and }f(b)

Tags

Differential calculus
Continuity
Definition

Detail

Intermediate value theorem (qualitative statement).

Explore the idea

Explore the idea

Variables

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

Found an error? Contact us.

Related formulas

Related
Formula
$f\text{ is continuous at }a \quad\Longleftrightarrow\quad \lim_{x\to a}f(x)=f(a)$
Open formula Open in section