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Overview
Calculus
10. Curve Analysis
10.1 Curve sketching
Curve Sketching in Calculus
Learn how derivatives reveal a function's true shape so you can sketch accurate graphs using critical numbers, concavity, and asymptotes.
What You'll Learn
Identify the domain, intercepts, and any symmetry of a function before analyzing its derivatives
Locate vertical and horizontal asymptotes by checking undefined points and end behavior
Find critical numbers by setting the first derivative equal to zero or undefined
Build a sign chart for the first derivative to determine increasing and decreasing intervals
Use the second derivative to identify concavity and locate inflection points
Combine domain, intercepts, asymptotes, extrema, and concavity into one accurate sketch
What You'll Practice
1
Finding domain restrictions and vertical asymptotes for rational functions
2
Calculating x-intercepts and y-intercepts by factoring and substitution
3
Performing first derivative tests to locate local maxima and minima
4
Applying the second derivative test to determine concavity and inflection points
5
Sketching complete graphs using all critical features and behavior analysis
Why This Matters
Curve sketching is a powerful calculus skill that connects derivatives to graph behavior. By mastering the 5-step approach, you gain deep insight into how functions behave, enabling you to analyze and visualize complex relationships in physics, engineering, economics, and beyond without relying solely on technology.
This Unit Includes
10 Video lessons
Learning resources
Skills
Curve Sketching
Derivatives
Critical Points
Concavity
Inflection Points
First Derivative Test
Second Derivative Test
Graph Analysis
GA Curriculum Aligned