The Lagrange Error Bound for Taylor Polynomials

In this video we go over what the Lagrange Error Bound is and how to find it. We go through each part in depth and then do an example to show how it works. It's not as bad as it seems!
You'll definitely need to know this for the AP Calculus BC exam. It's frequently on the free response section.

[@codyr9951]

Just wanted to say that this is probably one of the best videos I've found on the Lagrange Error Bound. Thank you.

[@bb-hf7el]

This is 5 million times better than sitting in a class for an hour and a half listening to your teacher read meaningless equations off a note packet. It feels good to actually be taught something somewhat complex by someone who actually cares to explain it.

[@turksvids]

I appreciate the comment! Good luck with your studies!

[@deusvult316]

based and redpilled

[@nameme6482]

This is REALLY HELPFUL. Thank you so much for doing this video.

[@fitocheeto4196]

probably the neatest explanation I've seen, thank you!

[@mohanprasad6373]

Well explained

[@ldswko]

Thank you so much ❤

[@AK47_414]

How do you find M. I didn’t understand how you got 24 for M. Please help

[@turksvids]

You're looking for the maximum of 24(1+x)^(-3) on the interval from 0 to 0.2. Since 24/(1+x)^3 is a decreasing function, the maximum will occur at the left endpoint, which is x=0. So the maximum is 24/(1+0)^3 = 24. Hope this helps!

[@AK47_414]

@@turksvids thanks. But how do I know if a function is decreasing or increasing just by looking at it?

[@turksvids]

Well you have two options. First is to think it through: the numerator is constant while the denominator gets bigger so overall the fraction will decrease in size. The other option is to just find the derivative and you'll see that the derivative is always negative on that interval so its function is decreasing.

[@Anna-qp1fi]

This explained the Lagrange error bound perfectly! Thank you for going down to a reasonable depth, it shows that you have had good teachers in your life...thank you for passing them onto us :) Keep up the great content!

[@jaice0447]

this video was so helpful man. Thank you so much

[@SamStarrs]

Lets get this bread tomorrow 😤

[@rosey6851]

Really helpful and detailed video. Thank you

[@pranavmadhukar12]

This video is amazing! I had a question on the calculator function that you showed at the end of the video. Which calculator do you use? And is that function necessary? Because I use a TI84, and I don't think it has that true/ false statement function.

[@turksvids]

Thanks! I use a TI-Nspire CX II CAS (long name...). The thing I did at the end is definitely not necessary. I was just showing how the inequality is true for that example.

[@pranavmadhukar12]

@@turksvids got it. Thanks!

[@sundamsoomro4332]

What an amazing video! So well made: concise, clear, easy to follow and relevant! Probably the best video on this topic on TH-cam and trust me I've been searching all day lol. Subscribed!

[@turksvids]

thanks! good luck with your studies!

[@burtonstudios5223]

By far the best explanation I have found on this topic, great work!

[@belenseoane]

THANK YOU

[@theunknown4209]

that makes so much sense. clear, to the point, well stated

[@rikijackson614]

MY AP CALC BC EXAM IS TMR AND YOU SAVED ME THANK YOU

[@fionamulderrig8936]

sooo real i’m doing last min review😭😭

[@manusaini13]

Great Video, thanks

[@milespiano]

bruhh you didn't explain why it works lol thats what i was looking for XD

[@turksvids]

sorry it wasn't the video you were hoping for!

[@hyperdimensionallight4931]

This is so great!

[@turksvids]

Thanks! Please share with anyone you think could benefit!