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

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Subtitles are provided through the generous assistance of Jimmy Ren.

Category:

Education

Tags:

• Gilbert Strang
• Gil Strang
• introduction
• intro
• calculus
• Highlights for High School
• MIT OpenCourseWare

[x1x2x3ct]

but those are just words... the graphs are telling us much more than the words do.

[mclaarson]

Thank you Professor for all your hard work.

[luis12181]

Thanks. One of the most simple, and brilliant explanations regarding this subject.

[savadelis]

@rr5001 i think because he was using sinx and cosx. always defined in his beginning examples

[kishorkryptonite]

Thank you Professor Strang ,you have helped me a lot.

[karlsmithbynre]

'If I knew where we were (22:58) mathematics would even more useful than it is...which would be hard to do!' This guy is fantastic.

[rr5001]

can someone plz tell me if there was a reason he didn't mention a critical number exists also when the function is undefined? also, in his example from home to mit, why is b constant????

[rr5001]

can someone plz tell me if there was a reason he didn't mention a critical number exists also when the function is undefined?

[LAnonHubbard]

Thanks Professor Strang.

[storaman12]

Thank you