I need to calculate the taylor polynomial T2(x) at 1 for the function

f(x) = x/1+2x

I have the following, with some blanks can anyone help?

For this function

f(x) = x/1+2x, f(1) = 1/3

F'(x) = ? f'(1) = ?

F"(x) = ? f"(1) = ?

Hence the Taylor polynomial of degree 2 at 1 for f is

T2(x) = 1/3 ? (x-1) ? (x-1)^2

Then I need to show that T2(x) approximates f(x) with an error less than 1/30 on the interval [0.5,1.5].

I have with I=[0.5,1.5], a=1,r=1,n=2.

1.First, f^(3) (c) = ?

2. Thus |f^(3) (c)|= ? for c E [0.5,1.5]

so we take M =

3. Using the remainder estimate (M/(n+1)!r^n+1,

we obtain

|f(x)-T2(x)| = |R2(x)|

equalor more than M/(2+1)! r^2+1

=1/3! * ? * 1^3

= ? = ? for x E [0.5,1.5]

Thus T2(x) approximates f(x) with an error less than 1/30 on [0.5,1.5].