Concavity of Parametric Curves | Calculus 2 Lesson 41 - JK Math

Описание: How to Find Concavity of Parametric Curves (Calculus 2 Lesson 41)

In this video we learn about how to determine concavity at specific values of t and how to find t intervals of concavity for parametric curves (plane curves) using the second parametric derivative. We review the concept of concavity from Calculus 1 and then apply it to curves defined with parametric equations so that we can determine where they are concave up or concave down.

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This video series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!

Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!


Video Chapters:
0:00 Concavity of Parametric Curves
4:20 Example 1 Part 1 - Concavity at t=1 for x=t^2, y=(8/3)t^3
8:40 Example 1 Part 2 - Intervals of Concavity for x=t^2, y=(8/3)t^3
10:12 General Process for Finding Intervals of Concavity
13:34 Example 2 Part 1- Second Derivative for x=1+t^2, y=2t^3+t^4
17:33 Example 2 Part 2 - Intervals of Concavity for x=1+t^2, y=2t^3+t^4
25:15 Outro


📝 Examples Video:    • Concavity of Parametric Curves Examples | ...  

⏩ Next Lesson:    • Area Under Parametric Curves | Calculus 2 ...  

📺 Calculus 2 Playlist:    • Calculus 2  

📺 Calculus 1 Playlist:    • Calculus 1  


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