Can someone explain to me how to do this problem please?
Any help would be greatly appreciated!
Thanks in advance!
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)?