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: 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