1. ## Taylor remainder function

1. The problem statement.

I have to estimate the absolute value of the remainder, R2,x0=4(x), of the function f(x)=1/x1/2 on the interval ] 3.8 , 4.2 [ when x0 = 4 and n = 2.

2. Relevant equations

I've used this equation :

3. The attempt at a solution

I hope that someone will be able to look at this and help me because I think the result might be wrong, the absolute value of the remainder seems too small !

2. ## Re: Taylor remainder function

I think your calculations are pretty much correct, but you used the 3rd derivative instead of the 4th. Also your bounds are not really right. Here's more discussion:

3. ## Re: Taylor remainder function

No I don't want the 4th derivative because n = 2 and according to the equation I'm using I need the n+1 = 2 + 1 = 3th derivative.

4. ## Re: Taylor remainder function

Sorry, for some reason I read n = 3. You should read the previous note to see a correct determination of bounds for a remainder. Generally, you need to consider properties of the function $\displaystyle f^{(n+1)}(x)$ and $\displaystyle (x-a)^{n+1}$