The Second Partials Test & Saddle Points | Calculus 3 Lesson 53 - JK Math
How to Use The Second Partials Test for Multivariable Functions (Calculus 3 Lesson 53) ➡️ Download my FREE Multivariable Functions Cheat Sheets: https://www.jkmathematics.com/multiva... 🖥️ Membership Site (community & bonus content): https://www.jkmathematics.com/plus 🌐 My Website: https://www.jkmathematics.com ⭐️ Support Me on Patreon: / jkmath In this video you will learn about identifying critical points of multivariable functions as relative extrema or saddle points by using the second partials test. We first introduce the formula for the test, and then practice using it with a couple examples. This video series is designed to help students understand the concepts of Calculus 3 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 3 requires a solid understanding of concepts from calculus 2, calculus 1, precalculus, and algebra. This includes limits, differentiation, advanced integration techniques, applications of derivatives and integrals, polar coordinates, parametric equations, trigonometric functions, logarithms, factoring, equation manipulation, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first! Video Chapters: 0:00 Recap of Extrema in 3D 4:04 The Second Partials Test 7:57 How the Formula Makes Sense 18:17 4 Step Process 19:28 Example: f(x,y)=x²+6y²+x²y+2y^3 36:18 Example: f(x,y)=x²y² 📝 Examples Video: • The Second Partials Test Examples | Calcul... ⏩ Next Lesson: • Absolute Extrema for Regions in 3D Space |... 📺 Calculus 3 Playlist: • Calculus 3 📺 Calculus 2 Playlist: • Calculus 2 📺 Calculus 1 Playlist: • Calculus 1 ⚡️Math Products I Recommend⚡️ Graphing Calculator: https://amzn.to/3XuUcB9 Non-Graphing Calculator: https://amzn.to/46hHJ7E Financial Calculator: https://amzn.to/3CRe9s4 Graphing Paper: https://amzn.to/46mAfAr College Rule Paper: https://amzn.to/3NOJaTN My Favorite Pencil: https://amzn.to/3NOFMIB My Favorite Erasers: https://amzn.to/3PumUQB Calculus Workbook: https://amzn.to/3r8SnNP ⚡️Textbooks I Use⚡️ Calculus 1 & 2: https://amzn.to/3PzfI5F Calculus 3: https://amzn.to/46rSy76 Financial Mathematics: https://amzn.to/3ppIVW0 Algebra: https://amzn.to/3Eaq1cy ⚡️My Recording Equipment⚡️ iPad Air: https://amzn.to/3phEug1 Apple Pencil (Gen 2): https://amzn.to/3Nl45MM Tablet Desk Stand: https://amzn.to/4420rPh External Hardrive: https://amzn.to/44pkEyh (Commissions earned on qualifying purchases) Found this video to be helpful? Consider giving this video a like and subscribing to the channel! Thanks for watching! Any questions? Feedback? Leave a comment! Josh from JK Mathematics #calculus Disclaimer: Please note that some of the links associated with the videos on my channel may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.