Max and Min and Second Derivative

Instructor:
Prof. Gilbert Strang

Resources:
Summary with practice problems
(PDF with audio - 2.2MB)
(MP3 - 2.2MB)

Practice problems
(PDF no audio)

Free downloads:
Internet Archive (MP4 - 172MB)
iTunes U (MP4 - 84MB)

Professor Strang's Calculus textbook (1st edition, 1991) is freely available here.

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At the top and bottom of a curve (Max and Min), the slope is zero. The "second derivative" shows whether the curve is bending down or up. Here is a real-world example of a minimum problem:

What route from home to work takes the shortest time?