3rd Degree Taylor Polynomial

s3a

Nov 2008
624
5
Can someone explain to me how to do this problem please?

Any help would be greatly appreciated!
Thanks in advance!
 

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s3a

Nov 2008
624
5
If it were a problem of the form 1/(1-x) I'd know what to do but it isn't. Any ideas?
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
This is very peculiar- you use the terms "Taylor Polynomial" and "Taylor Series" but your questions imply that you don't know the definition or formula!

The "third degree Taylor Polynomial" for function f(x) about x= a is
\(\displaystyle \frac{f'''(a)}{3!}(x- a)^3+ \frac{f''(a)}{2!}(x- a)^2+ \frac{f'(a)}{1}x+ f(a)\).

Here, \(\displaystyle f(x)= (7x+ 228)^{5/4}\). \(\displaystyle f(4)= (28+ 228)^{5/4}= 4^5= 1024\).

\(\displaystyle f'(x)= \frac{5}{4}(7x+ 228)^{1/4}(7)= \frac{35}{4}(7x+ 228)^{1/4}\) so \(\displaystyle f'(4)= \frac{35}{4}(28+ 228)^{1/4}= 35\).

Can you get f''(4) and f'''(4)?
 
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s3a

Nov 2008
624
5
I am VERY confused with this topic. I don't see how f^(n) (a) (x-a)^n /n! relates with taking 3 derivatives of f(x).
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
Now you've got me confused!

What do you think "\(\displaystyle f^{(n)}\)" means?