Relative and Absolute Maximums and Minimums | Part II

Learning Objectives:
1) Define Critical Points
2) For a function, compute the critical points
3) Construct examples of functions with and without extrema

Now it's your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!

Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master calculus means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.

This video is part of a Calculus course taught by Dr. Trefor Bazett at the University of Cincinnati.

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[itsjustniklas]

Montage = Awesome. Thanks for your great videos, you rock dude!

[selfstudypk]

this is the only math channel which have zero dislike on more than 90% videos i guess

[madghostek]

Awesome video, cleared some things up, the two questions were spot-on

[Hcs]

Thanks so much for these excellent videos!

[toomanycharacter]

We can model the graph around x1 using the tangent line very well for small enough scales, as we have seen in the linear approximations video.
So, if f(x) is continuous around x1 and f'(x1) != 0, the the tangent line at x1 will be higher than f(x1) in one direction, and lower in the other direction. For instance, for a positive derivative, the slope is going to be positive, so the tangent line will take values greater than f(x1) to the right, and lower than f(x1) to the left.
But since the tangent line approximates the graph, we then know, that the values of f(x) must also go up to one side of x1, and down to the other side! Obviously, then, x1 is not a local minimum/maximum.

[motivationformuslims]

beautifully explained and structured video. Thanks

[talhakhalid]

Prof are you taching according to the thomas calculus topics