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
» Clip 1: Minimal Surface Area of a Box: Direct Solution (00:21:00)
From Lecture 12 of 18.01 Single Variable Calculus, Fall 2006
Clip 1: Minimal Surface Area of a Box: Direct Solution
> Download from iTunes U (MP4 - 110MB)
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» Clip 2: Minimal Surface Area of a Box: Implicit Differentiation (00:05:00)
From Lecture 12 of 18.01 Single Variable Calculus, Fall 2006
Clip 2: Minimal Surface Area of a Box: Implicit Differentiation
> Download from iTunes U (MP4 - 110MB)
> Download from Internet Archive (MP4 - 110MB)
Recitation Video
Maximum Surface Area
> Download from iTunes U (MP4 - 19MB)
> Download from Internet Archive (MP4 - 19MB)
Worked Example
Can Design