#Taylor remainder

1 messages · Page 1 of 1 (latest)

soft wasp
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this is the Taylor poly

image.png
rigid tuskBOT
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soft wasp
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when i did my calc

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this is the upper boundary i got

image.png
chrome apex
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It depends on the function doesn't it

soft wasp
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oh sorry

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i am an idiot

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i forgot to post it

chrome apex
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What is the expression of the remainder?

soft wasp
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i used this formula

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the taylor poly is centered around 0

image.png
chrome apex
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I would have thought the remainder is a series

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Well never mind that

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Do you have an upper bound for the third derivative?

soft wasp
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yeah

soft wasp
chrome apex
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No I mean how did you derive an upper bound of the third derivative

soft wasp
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ohh

chrome apex
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On [a, x]

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Cause that's what we care about right

soft wasp
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yes

chrome apex
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Since c is somewhere in between

soft wasp
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i set the function to 0 and then applied the quadratic formula

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and found two zeros

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one of the points was outside [0,1], so i didn't use it

chrome apex
soft wasp
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yes

chrome apex
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Did you make sure that it was not a local min?

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The critical point I mean

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Because it might be that the max is at a bound

soft wasp
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i graphed on desmos

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but i didn't check it manually no

chrome apex
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Ok, sure

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Otherwise just compute the second derivative of f³

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At your critical point

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It's not too much of a tedious check I think

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Other than that I have nothing to complain about regarding the method itself

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It is logically sound

soft wasp
soft wasp
chrome apex
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So good job on that

potent canopyBOT
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@soft wasp has given 1 rep to @chrome apex

soft wasp
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+close