Session 30: Optimization Problems II

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Overview

The maximum and minimum values of a function may occur at points of discontinuity, at the endpoints of the domain of the function, or at a "critical point" where the derivative of the function is zero. To determine whether a critical point is a global maximum or minimum we compare the value of the function at that point to its value at the other candidates for minima and maxima.

Lecture Video and Notes

Video Excerpts

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» Clip 1: Minimal Surface Area of a Box: Direct Solution (00:21:00)

» Accompanying Notes (PDF)

From Lecture 12 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 2: Minimal Surface Area of a Box: Implicit Differentiation (00:05:00)

» Accompanying Notes (PDF)

From Lecture 12 of 18.01 Single Variable Calculus, Fall 2006

Recitation Video

 

Maximum Surface Area

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Worked Example

 

Can Design

 

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