Listen Top Shows Blog

Local Extreme Values and the Mean Value Theorem Part 1 - Rolle’s Theorem

Local Extreme Values and the Mean Value Theorem Part 1 - Rolle’s Theorem

Update: 2023-05-28

Share

Description

Having defined the derivative of a function in the previous episode, we now turn to properties of the derivative and of the function in connection to the derivative. This episode is concerned with a first theorem asserting as much, namely Rolle’s theorem. This theorem tells us that the derivative of a differentiable function has a zero as long as it assumes one value twice. A consequence of this will be the mean value theorem, the consequences of which we address in the next episode.

Picture from https://www.flickr.com/photos/11703832@N08/16827652499

Comments

In Channel

Integral and Differentiation — The fundamental theorem Part 2

Integral and Differentiation — The fundamental theorem Part 2

2023-07-1618:12

Integral and Differentiation — The fundamental theorem Part 1

Integral and Differentiation — The fundamental theorem Part 1

2023-07-0912:33

The Riemann Integral Part 4 - Monotonicity of the integral

The Riemann Integral Part 4 - Monotonicity of the integral

2023-07-0209:38

The Riemann Integral Part 3 - Monotone functions are Riemann integrable

The Riemann Integral Part 3 - Monotone functions are Riemann integrable

2023-06-2509:39

The Riemann Integral Part 2 - Riemann integrability

The Riemann Integral Part 2 - Riemann integrability

2023-06-1821:34

The Riemann Integral Part 1 - Step functions

The Riemann Integral Part 1 - Step functions

2023-06-1120:10

Local Extreme Values and the Mean Value Theorem Part 2 - Consequences of the Mean Value Theorem

Local Extreme Values and the Mean Value Theorem Part 2 - Consequences of the Mean Value Theorem

2023-06-0411:35

Local Extreme Values and the Mean Value Theorem Part 1 - Rolle’s Theorem

Local Extreme Values and the Mean Value Theorem Part 1 - Rolle’s Theorem

2023-05-2811:50

Differentiation Part 2 - Derivatives

Differentiation Part 2 - Derivatives

2023-05-2115:50

Differentiation Part 1 - Differentiability

Differentiation Part 1 - Differentiability

2023-05-1510:02

Complex Exponentials, trigonometric functions Part 4 - What is pi ?

Complex Exponentials, trigonometric functions Part 4 - What is pi ?

2023-02-2716:06

Complex Exponentials, trigonometric functions Part 3 - Euler's formula

Complex Exponentials, trigonometric functions Part 3 - Euler's formula

2023-02-2013:43

Complex Exponentials, trigonometric functions Part 2 - The Exponential Function with Complex Arguments

Complex Exponentials, trigonometric functions Part 2 - The Exponential Function with Complex Arguments

2023-01-2320:25

Complex Exponentials, trigonometric functions Part 1 - The miracle of i

Complex Exponentials, trigonometric functions Part 1 - The miracle of i

2023-01-1717:58

Monotone Functions, Inverse Functions, Logarithm, General Power Part 4 - Continuity of the Inverse Function

Monotone Functions, Inverse Functions, Logarithm, General Power Part 4 - Continuity of the Inverse Function

2022-12-1318:25

Monotone Functions, Inverse Functions, Logarithm, General Power Part 3 - Uniqueness of General Powers

Monotone Functions, Inverse Functions, Logarithm, General Power Part 3 - Uniqueness of General Powers

2022-12-0513:00

Monotone Functions, Inverse Function, Logarithm, General Power Part 2 - Existence of General Powers

Monotone Functions, Inverse Function, Logarithm, General Power Part 2 - Existence of General Powers

2022-11-2912:59

Monotone Functions, Inverse Functions, Logarithm, General Power Part 1 - The Logarithm

Monotone Functions, Inverse Functions, Logarithm, General Power Part 1 - The Logarithm

2022-11-2213:39

Theorems about Continuous Functions Part 3 - Uniform Continuity

Theorems about Continuous Functions Part 3 - Uniform Continuity

2022-11-1515:49

Theorems about Continuous Functions Part 2 - Invariance of Sequential Compactness and the Extreme Value Theorem

Theorems about Continuous Functions Part 2 - Invariance of Sequential Compactness and the Extreme Value Theorem

2022-11-0811:33

00:00

00:00

x

Local Extreme Values and the Mean Value Theorem Part 1 - Rolle’s Theorem

Local Extreme Values and the Mean Value Theorem Part 1 - Rolle’s Theorem

profmoppi