Question

Find the Taylor series at
a = −4 for f(x) = x4 + 5x2 + 5.

Answer 1

It's an e^x... but yeah, I don't know where to go from here.

Answer 2

I think you have to use this.
\[ \Large
\sum_{n=0}^\infty f^{(n)}(a)\frac{(x-a)^n}{n!}
\]Where \(f^{(n)}(a) \) is the nth derivative evaluated at a.

Answer 3

I tried that... it's only the first derivative if it asks it like it does?

Answer 4

? only the first derivative?

Answer 5

You do keep doing the derivative until you have a pattern or get to 0

Answer 6

\[
\begin{array}{l}
f^{(0)} = x^4+5x^2+5 \\
f^{(1)} = 4x^3+2*5x \\
f^{(2)} = 4*3x^2+2*5 \\
f^{(3)} = 4*3*2x \\
f^{(4)} = 4*3*2 \\
f^{(5)} = 0 \\
\end{array}
\]

Answer 7

Not sure what you mean by it's an \(\large e^x\).

Answer 8

Nevermind, I am being retarded, I got it :) Thank you