Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Derivability and Tangents

Description

This lecture covers the concept of derivability, tangents, and the theorem of Rolle. It explains how to determine the slope of a tangent line and the linear approximation of a function. The lecture also discusses the theorem of finite increments and its application in calculating derivatives.

Official source

Ontological neighbourhood

Mathematics

Analysis: Calculus

Related concepts (32)

Linear approximation

In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations. Given a twice continuously differentiable function of one real variable, Taylor's theorem for the case states that where is the remainder term.

Adobe Illustrator

Adobe Illustrator is a vector graphics editor and design program developed and marketed by Adobe Inc. Originally designed for the Apple Macintosh, development of Adobe Illustrator began in 1985. Along with Creative Cloud (Adobe's shift to a monthly or annual subscription service delivered over the Internet), Illustrator CC was released. The latest version, Illustrator 2023, was released on October 18, 2022, and is the 27th generation in the product line. Adobe Illustrator was reviewed as the best vector graphics editing program in 2021 by PC Magazine.

Adobe Photoshop

Adobe Photoshop is a raster graphics editor developed and published by Adobe Inc. for Windows and macOS. It was originally created in 1987 by Thomas and John Knoll. Since then, the software has become the most used tool for professional digital art, especially in raster graphics editing. The software's name is often colloquially used as a verb (e.g. "to photoshop an image", "photoshopping", and "photoshop contest") although Adobe discourages such use.

Rolle's theorem

In calculus, Rolle's theorem or Rolle's lemma essentially states that any real-valued differentiable function that attains equal values at two distinct points must have at least one stationary point somewhere between them—that is, a point where the first derivative (the slope of the tangent line to the graph of the function) is zero. The theorem is named after Michel Rolle.

Mean value theorem

In mathematics, the mean value theorem (or Lagrange theorem) states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints. It is one of the most important results in real analysis. This theorem is used to prove statements about a function on an interval starting from local hypotheses about derivatives at points of the interval.

Related lectures (37)

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Derivatives and Local Extrema

Explores derivatives, local extrema, and function variation in mathematical analysis.

Derivatives: Definition and Properties

Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Derivatives and Reciprocal Functions

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.

Derivatives and Continuity in Mathematics