Proof By Contradiction - Calculus Based Example

Proof By Contradiction - Calculus Based Example. In this video, I use proof by contradiction along with some calculus results to justify a function has exactly one real root.
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Category:

Education

Tags:

• math
• calculus
• proof
• by
• contradiction
• rolle
• theorem
• mean
• value
• exactly
• one
• root
• justmathtutoring.com
• AP
• BC
• GRE

[pouchmaster69]

PatrickJMT, helping me in through my calculus classes, and now helping me with my discrete math class. You sir, are a jack of all trades.

[patrickJMT]

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

[tombert256]

This is pretty cool. I've always wanted to learn how to do these types of proofs...they seem to breeze over these things in my calc classes.

I like all your videos. They can be extremely helpful, and honestly, they are somewhat pleasant to watch.

[patrickJMT]

who'da thunk?

math, pleasurable....

[tombert256]

I told my calc BC class about you a few days ago, since we were all having a bit of trouble with finding the radius and endpoints of convergence.

I don't know if your videos helped them, but I have no reason to think they wouldn't.

[patrickJMT]

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

[duyu]

My appreciation for your videos can be contradicted by nothing!

[grlaer]

What about the use of Rolle's theorem? Where does that come into play?

[JThorss0N]

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).

[arsenalwak]

2.. 3.. 20 times, haha what a legend ;)

[Stavers50]

you're left-handed too! Makes you even cooler

[duhboss1]

I really like this video. You do a solid job of showing what a powerful tool calculus can be.

[sugarcoatedsour]

It would have been better to use Rolle's Theorem since you are looking for roots, because Rolle's theorem specifically states that f'(c')=0 and since the derivative of the given function is never less than 2, it would be a contradiction. IMHO.

[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.

[mudgalsourabh348]

its a pretty nice way of solving a mathematical problem