Multi-variable Optimization & the Second Derivative Test

Pubblicato il: 24 novembre 2019
sul canale di: Dr. Trefor Bazett

150,592

4.2k

Finding Maximums and Minimums of multi-variable functions works pretty similar to single variable functions. First,find candidates for maximums/minimums by finding critical points. Critical Points are where the partial derivatives with respect to x and y are both zero. Then we classify each critical point using the second derivative test. In the multivariable case, there is a new option beyond max/min/neither, there is also the case of the saddle point. The second derivative test involves computing the Hessian, the determinant of a matrix that helps decide whether points are maximums/minimums/saddle or inconclusive. We sketch the geometric intuition behind the Hessian.

****************************************************
YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems!
****************************************************
►Full Multivariable Calculus Playlist:    • Calculus III: Multivariable Calculus (Vect...

****************************************************
Other Course Playlists:

►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...

► CALCULUS II:    • Calculus II (Integration Methods, Series, ...

►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...

►LINEAR ALGEBRA:    • Linear Algebra (Full Course)

***************************************************

► Want to learn math effectively? Check out my "Learning Math" Series:
   • 5 Tips To Make Math Practice Problems Actu...

►Want some cool math? Check out my "Cool Math" Series:
   • Cool Math Series

****************************************************
►Follow me on Twitter:   / treforbazett

*****************************************************

This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.

BECOME A MEMBER:
►Join:    / @drtrefor

MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett

In questa pagina del sito puoi guardare il video online Multi-variable Optimization & the Second Derivative Test della durata di 13 minuti 36 seconda in buona qualità , che l'utente ha caricato Dr. Trefor Bazett 24 novembre 2019, condividi il link con amici e conoscenti, su youtube questo video è già stato visto 150,592 volte e gli è piaciuto 4.2 mille spettatori. Buona visione!

54,509