Suppose we want to find the maximums and minimums of a function. Previously in our Calc III playlist we saw how to do this with the second derivative test. But what if we demand that are optimizing on a closed, bounded region? That is, a region that has a boundary. Similar to first year calculus, the idea is that the maximums and minimums either occur in the interior of the region (found by analyzing critical points with the second derivative test), OR the extrema occur along the boundary. In this video we will learn how to do this process along the boundary. **************************************************** COURSE PLAYLISTS: ►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...   ► CALCULUS II:    • Calculus II (Integration Methods, Ser...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus ...   ►DIFFERENTIAL EQUATIONS (Calc IV): https://www.youtube.com/watch?v=xeeM3TT4Zgg ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Log...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   *************************************************** ► Want to learn math effectively? Check out my "Learning Math" Series: https://www.youtube.com/watch?v=LPH2lqis3D0 ►Want some cool math? Check out my "Cool Math" Series:    • Cool Math Series   **************************************************** ►Follow me on Twitter: http://twitter.com/treforbazett ***************************************************** This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria. BECOME A MEMBER: ►Join: null MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett