Solving Interpolation Error w/ ≤ 5*10-8 Precision

[peripatein]

Hi,

Homework Statement

Interpolation for the function f(x)=cos(x) for evenly distributed values of x in [0,π] (h=x_i+1-x_i, x_i=ih, i=0,1,...,πh) is carried out. Also known are f(x_i).
I am asked to determine the value of h so that the interpolation's error is ≤ 5*10^-8.

Homework Equations

The Attempt at a Solution

I have found f'''(x) for x in [0,π] to be ≤ 1.
Now I am stuck with evaluating |(x-x_i+1)(x-x_i)(x-x_i-1)|.
I'd truly appreciate some assistance. Thanks in advance!

 

[peripatein]

I have managed on my own with this one. Thank you in any case :).