Multi-variable Optimization & the Second Derivative Test
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
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