18.01SC | Fall 2010 | Undergraduate

Single Variable Calculus

Part A: Approximation and Curve Sketching

Session 27: Sketching Graphs I - Polynomials and Rational Functions

« Previous | Next »


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

Clip 1: Introduction to Curve Sketching

Clip 2: Example: 3x-x3

Clip 3: Graphing a Rational Function

Recitation Video

Sketching a Curve

« Previous | Next »

Course Info

As Taught In
Fall 2010
Learning Resource Types
Exams with Solutions
Lecture Notes
Lecture Videos
Problem Sets with Solutions
Recitation Videos