I just want to make sure I'm doing this right.

So we're given the funciton

we're first asked to find the 4th degree taylor polynomial centered at

we're then asked to use taylor's inequality to bound the error in the approximation

we recall

well,

so i'd want to use

?

if i understand correctly, I want M to be as big as possible. and since this is centered at a=1, this would give me

this just seems like quite a big maximum error to me.

if someone could confirm that this is the error i should be getting, that'd be great.