Highlights of Calculus - Max and Min and Second Derivative

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? View the complete course at: http://ocw.mit.edu/highlights-of-calculus 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 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu Subtitles are provided through the generous assistance of Jimmy Ren.