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Chapter 3.5
Curve sketching
What You'll Learn
Apply the 5-step approach to systematically sketch the graph of any function
Determine domain, intercepts, and asymptotes for rational and polynomial functions
Use the first derivative to find critical points and intervals of increase/decrease
Use the second derivative to identify concavity and inflection points
Combine derivative information to sketch accurate graphs without a calculator
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
Skills
Curve Sketching
Derivatives
Critical Points
Concavity
Inflection Points
First Derivative Test
Second Derivative Test
Graph Analysis
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