# Math Help - taylor polynomial

1. ## taylor polynomial

i cant believe i got this wrong but I did and I dont know why.

find the 2nd order Taylor Polynomial of $f(x)= cos(x^2)$ centered at zero

f(x) = cos x , then f(0) = 1
f'(x) = -sinx, f'(0) =0
f"(x) = -cosx f"(0) = -1

second order TP of cosx is:
$1 + 0x - \frac{x^2}{2!}$

Replace x with x^2, second order TP of $cos(x^2)$ :
$1 - \frac{x^4}{2!}$

But my book says that P"(x) = 1
What gives?

2. ## Re: taylor polynomial

Originally Posted by delgeezee
But my book says that P"(x) = 1
What is P and at which x do you take the derivative?

Your polynomial is correct; see WolframAlpha.

3. ## Re: taylor polynomial

Thanks for the Web site! This will help me study more efficiently.