Curve Sketching | Calculus Lesson 26 – JK Math

How to Sketch Curves Using Calculus (Calculus Lesson 26)

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In this lesson we learn about how to sketch the graph of a function using various techniques learned across algebra and calculus. We look at step-by-step process of what needs to be done in order to accurately sketch the graph of a function. This includes:

– Domain / Continuity / Asymptotes
– x- and y-intercepts
– Relative Extrema / First Derivative Test
– Infection Points / Concavity

Together, all these concepts allow us to sketch the graph of a function. We look at one example in this video showcasing each of these steps and how they help us sketch curves.

📺 Lesson Links (Referenced in beginning of the video) 📺
Continuity (Lesson 5): https://youtu.be/1yw0tzUY6vc
Limits at Infinity (Lesson 7): https://youtu.be/TgW5jKtFETY
Extrema on an Interval (Lesson 19): https://youtu.be/yQnAPgS2hnY
Increasing & Decreasing Functions (Lesson 22): https://youtu.be/fp6AmBM_frM
The First Derivative Test (Lesson 23): https://youtu.be/6CUKfuDJz4k
Concavity (Lesson 24): https://youtu.be/BSv67aWVBaA

[NOTE]: Due to the amount of work involved with sketching the graph of a curve, I needed to make a one-time exception to my “each lesson under 20 minutes” promise for Calculus 1 videos. Many attempts were made to create a version of this lesson that was under 20 minutes, but the quality of that version did not meet the standards that I strive to meet with each lesson. A lot of corners would have been cut, and a lot of steps would have been skipped, which I believe ultimately would have resulted in a less helpful and half-baked video.

This course is designed to help students understand the concepts of calculus at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with each lesson under 20 minutes! (Except this one, sorry!)

Calculus requires a solid understanding of precalculus and algebra concepts and techniques including factoring, equation manipulation, trigonometric equations, logarithms, finding slope, graphing, and many more. If you are not familiar with these prerequisite topics, be sure to learn them first!

Video Chapters:
0:00 Overview of the Curve Sketching Steps
2:05 First Derivative Review
2:49 Second Derivative Review
3:41 Curve Shape Chart
5:10 Example Part 1- Domain & Continuity
6:31 Example Part 2- Vertical Asymptotes
7:12 Example Part 3- Horizontal Asymptotes
9:05 Example Part 4- x-intercepts
10:14 Example Part 5- y-intercept
11:28 Example Part 6- First Derivative
13:47 Example Part 7- Differentiability
14:16 Example Part 8 – Critical Values
15:02 Example Part 9 – First Derivative Test
18:33 Example Part 10 – Second Derivative
21:34 Example Part 11 – Inflection Points & Concavity
24:52 Example Part 12 – Combining Number Lines
26:43 Example Part 13 – Curve Sketching

📝 Example Video: https://youtu.be/HHTQlYYk_Gc

⏩ Next Lesson: https://youtu.be/hT6jY757WCg

📺 Course Playlist: https://youtube.com/playlist?list=PLHdRLeAbIZE6krGDQthaQRpLZFLD4ob54

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-Josh from JK Math

#calculus

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