# 3rd Degree Taylor Polynomial

#### s3a

Can someone explain to me how to do this problem please?

Any help would be greatly appreciated!

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#### s3a

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
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

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
Now you've got me confused!

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