Curve sketching summary lesson for Calculus with guided notes, homework, and video lesson. Teach graph analysis using intercepts, asymptotes, derivatives, critical values, inflection points, and concavity.

This is one lesson from my Calculus Unit 3 – Applications of Derivatives curriculum. It includes guided notes, homework practice, a full video lesson, and detailed step-by-step answer keys to support student understanding.

This lesson is designed for a guided, non-AP Calculus course and works well for honors-level high school calculus or introductory calculus classes. The structure helps students put together first derivative, second derivative, asymptote, and intercept information to sketch functions.

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☑️ Continue with Calculus 3.6 - Graphical Analysis of a Function and Its Derivative

💜 Topics Covered in This Lesson

• Curve sketching summary

• x-intercepts and y-intercepts

• Vertical asymptotes

• Horizontal asymptotes

• Slant asymptotes

• First derivative

• Second derivative

• Critical values

• Points of inflection

• Relative extrema

• Intervals of increase and decrease

• Intervals of concavity

• Sketching many different types of functions

💜 What’s Included

• Guided notes

• Homework practice (8+ problems)

• 8+ worked examples

• Full video lesson (walks through notes and examples)

• Detailed step-by-step answer key

💜 Perfect For

• High school Calculus

• Honors Calculus

• Introductory Calculus

• Non-AP Calculus courses

• Applications of derivatives units

• Curve sketching and graph analysis

• Teachers who want structured, guided instruction with video support

This lesson is designed to make teaching curve sketching more clear, organized, and manageable while helping students combine multiple calculus concepts into one graph analysis process.

I have been teaching high school math, mostly honors-level courses, in the private school system for over 25 years. After much success with my digital Algebra 2 curriculum with videos, I decided to create a non-AP Calculus curriculum with guided notes, video lessons, homework practice, and detailed answer keys to use with my own students and share with other teachers.

I hope this resource helps make teaching Calculus clearer, smoother, and more manageable for you and your students!

-Shira Strong

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