Proof By Contradiction - Calculus Based Example

[patrickjmt]

people confuse working really really hard with super natural talent. i was one of the hardest working undergraduates i know of.

[nikitavakoli]

thank you so much. this was explained really well 

[patrickjmt]

yep, for sure!
but as you pointed out, i am trying to make the idea of 'proof by contradiction' easy to understand.

[patrickjmt]

yes, is available in hd.

when i first post them, they appear for a few minutes without the hd feature for some reason

[patrickjmt]

@pouchmaster69 i always really liked the discrete stuff, i should do more videos on it

[rachbach]

Oh, Patrick! I have to thank you! Today, I took my last math exam ever and I'm pretty sure I aced it thanks to you! You're such an incredible teacher! Truly, I cannot thank you enough. I have referred a lot of my friends to your videos and they all love you too! You're the best math teacher ever!

[patrickjmt]

well hopefully i did not make them more clueless at least : )

[patrickjmt]

i took them at the same time with no problem.

[deborahleopo]

is there any way you write out a statement? my professor requires we write out a statement for examine
since f(x) is a polynomial is cont on [0, -1] etc...
i just need help phrasing a statement for rolles theorem please and thanks!

[patrickjmt]

who'da thunk?

math, pleasurable....

[BLAKEBOFFA]

Patrick, you got me through Calc 1, 2 and 3. It's been a while since I've watched your videos. I'm struggling in Advanced Calc now and this has been very helpful. Thank you so much for everything!

[fakwater]

I bought your Itouch app for calc 1 and was looking for some examples such as these, do you think you will link them up any time soon? BTW I stopped going to my math class because I learn more off your videos then i do in class. I currently have a B in my class.

[abuccilli]

Now that you have completed the problem and explained it logically, you should write the proof out, as if you were going to submit it for homework or it was going to be published.

[HCI]

He just tried 2 arbitrary number, normally it is easy to start with 0, 1, -1, 2, -2, ... and see if it gives us positive or number values for Y

[SarahJewell]

Oh hell yes that is THE problem I just worked!! But I needed to actually understand the significance of the contradiction, so thanks!

[Joojoo]

at the beginning when u used the IVT, how did u know to plug in 0 and -1 to find that the polynomial has 1 root?

[hmoobdaj]

wow
this is the same exact problem (numbers and everything) that was in the book....

[brianlogreco]

Bravo if that was all one long shot. I found your lecture to be very easy to follow along with it, more fluid; much better than Sal's

[Crow]

It seems as though we never use the portion of the mean value theorem that relates to the secant line, but instead take advantage of the fact that the function is continuous between a negative and positive value. Do we have to use the mean value theorem for this reason or is there another way to simply say that the function is continuous?

[JThorssN]

Great explanation! I think c should be in the open interval (r1, r2) though, because in both Rolle's theorem and the Mean value theorem you're assuming f is continuous in the closed interval [a, b] and differentiable in the open interval (a, b).