This is the question: What is the error in quadratic interpolation to $f(x)=1/x$, using equally spaced nodes on the interval $[1/2,1]$?
I used this $|f(x)-p_2(x)|\le1/(9\sqrt{3} )h^3 \max|f'''(t)|$ where $x_0 \le t\le x_2$
so, $f'''(x)= -6x^{-4}$.
So $\max|f'''(t)|= 6(1/2)^{-4} = 6\cdot2^4 = 96$
$|f(x)-p_2(x)|\le 1/(9 \sqrt{3} )h^3 (96)$
But the answer in the book is $|1/x-p_2| \le 1/(6\sqrt{3} ) = 0.9622504490\cdot10^{-1}$
I don't understand the answer they gave, can anyone please explain? And what did I do wrong in my solution?
Thanks.