Session 27: Sketching Graphs I - Polynomials and Rational Functions

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Overview

The first derivative of a function tells us whether its graph slopes up or down or is level. The second derivative tells us how that slope is changing. By combining this information with what we know about asymptotes, intercepts and plotting points we can sketch a pretty good graph of the function.

Lecture Video and Notes

Video Excerpts

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» Clip 1: Introduction to Curve Sketching (00:07:00)

» Accompanying Notes (PDF)

From Lecture 10 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 2: Example: 3x-x3 (00:15:00)

» Accompanying Notes (PDF)

From Lecture 10 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 3: Graphing a Rational Function (00:19:00)

» Accompanying Notes (PDF)

From Lecture 11 of 18.01 Single Variable Calculus, Fall 2006

Recitation Video

Sketching a Curve

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