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 realworld example of a minimum problem:

What route from home to work takes the shortest time?

View the complete course at: http://ocw.mit.edu/highlightsofcalc...

Chapters
00:00 Outline
00:24 The Second Derivative: The derivative of the derivative
01:43 Examples of Second Derivatives
08:00 Convex and Concave Curves
09:28 Locating the Maximum and Minimum and the Inflection Point
23:40 Application: Driving to Work, Finding the Minimum Time

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Subtitles are provided through the generous assistance of Jimmy Ren.