Find the degree 3 Taylor polynomial T3(x) of the function f(x)=(7x−1)^4/3 at a=4
I am having a really hard time figuring out these Taylor Polynomials.
Please help!

Question

Find the degree 3 Taylor polynomial T3(x) of the function f(x)=(7x−1)^4/3 at a=4
I am having a really hard time figuring out these Taylor Polynomials.
Please help!

amistre64 · Answer

find 3 or 4 derivatives right?

anonymous · Answer

I have f'(x)= (28/3)(7x-1)^(1/3)
f "(x)= (196/9) (7x-1)^(-2/3)
f3(x) = (2744/27) (7x-1)^(-5/3)

amistre64 · Answer

f = (7x−1)^4/3

f' = 4/3 7 (7x−1)^1/3

f'' = 4.1/3.3  7.7  (7x−1)^-2/3

f''' = 4.1.-2/3.3.3  7.7.7   (7x−1)^-5/3

amistre64 · Answer

evaluate those at x=4

amistre64 · Answer

$$T(x)=f(a)+f'(a)(x-a)+\frac1{2!}f''(a)(x-a)^2+\frac1{3!}f''(a)(x-a)^3+...$$

amistre64 · Answer

.... dropped a ' on that last notation

anonymous · Answer

thank you!! I had just missed my negative on the last derivative

amistre64 · Answer

good job then ;)  that hardest thing about calculus is the algebra lol