Session 25: Introduction to Quadratic Approximation

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Overview

Linear approximation uses the first derivative to find the straight line that most closely resembles a curve at some point. Quadratic approximation uses the first and second derivatives to find the parabola closest to the curve near a point.

Lecture Video and Notes

Video Excerpts

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» Clip 1: The Formula for Quadratic Approximation (00:03:00)

» Accompanying Notes (PDF)

From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 2: Explaining the Formula by Example (00:04:00)

» Accompanying Notes (PDF)

From Lecture 10 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 3: Quadratic Approximation at 0 for Several Examples (00:05:00)

» Accompanying Notes (PDF)

From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006

Worked Example

 

Comparing Quadratic Approximations and Calculator Computations

Recitation Video

 

Quadratic Approximation of an Exponential Function

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