Interpolation - Lagrange poly interpolation error bounds for approximations of functions

This video looks at the error bounds for Lagrange poly approximations of functions.

[@Deksudo]

Notes: We're searching for the absolute maximum value of g(x) WITHIN THE GIVEN INTERVAL, g(x) goes to positive infinity after the critical points but that's beyond our interval of (2,4) so it doesn't concern us. There's a small space between the critical points of the first derivative and the edges of our interval, [2, 7/3] and [7/2, 4] where the function itself could theoretically have an absolute value larger than the value at those points, but g(2)=0 and g(4)=0 (like he mentioned in the video), and both of these intervals are monotonically increasing, so g(7/3) is the maximum point within the interval, and g(7/2) the minimum point. The one that's bigger in terms of absolute-value will do. 6:20 g(7/3) is 25/108, not 25/10. He says the correct value but i guess he forgot to write the last digit idk. If anyone's confused why he choose 9/16 over 25/10 after saying the bigger one in terms of abs val. The mentioned book (9th edition) has a slightly different answer than the one here but i think they made a typo at the end and the solution in this video is the correct one. I'm downloading the 10th edition right now to see if they fixed that. Edit: 10th edition has the same solution as the video.

[@tiger5869]

you can tell it's good math by the poor handwriting

[@ngonidzashekimbini7177]

I discovered the complete series just in time Many thanks sir Love your accent btw

[@saquibsarwer526]

Awesome video bro❤

[@jaredtweed7826]

where does the 1/16 come from at 6:41?

[@nana00037]

4:37 f(n+1)th derivative of 2 = 1/2^(4) = 1/16 we take 2 because it's the largest value for the n+1 st derivative of f

[@candleclz]

dont we need to check for what value x=7/3 and x=7/2 will be max or min ?

[@solaymanebamou6552]

thank you prof.keep going

[@yoshiboy6198]

Thank you super helpful!

[@tovichallenger7469]

my guy I love you on god

[@gp7964]

Sir, in case that you have 3 values xo,x1,x2 and you dont want to use Lagrange bound error method , what choice do you have? How can one use these 3 values and fit them to Taylor remainder or elsewhere to aproximate the error? In any case thank you.

[@abbasbookwala]

why was 25/10 ignored and 9/16 adopted?

[@Saifullah-lw6he]

because 9/16>25/10 we have to take larger value

[@umer2465]

You forgot to mention the factorial term in the maximum bound error ξmax. The maximum bound error ξmax is ( 1/16 ) * ( 1/3! ) * ( 9/16 ) = 3/512 ≈ 0.00586. reference: Numerical Analysis by Burden and Faires (9th edition) example 3 of chapter 3

[@ranz2931]

1/16?

[@arshdeepsingh3397]

ara bahi hindi bola kar