Question: The function $f(x) =(1+x)^6$ is to be tabulated at equispaced points in the interval $[0.1]$ using quadratic interpolation. Find the largest step size that can be used used so that the error $\le 5 × 10^-3$ in magnitude.
Problem: Can we convert a polynomial of degree 6 into degree 2? Is it not going to completely change the result/nature of polynomial. I have solved these kind of problems but there the polynomial that was given was of degree 1 or less then 2 (eg:- $f(x)= \frac{1}{x} $ OR $f(x)= \sqrt{x}$).
Formula Used (for 2 degree polynomial): $|E|\le \dfrac{h^3M}{(9\sqrt{3})}$
Where: $M= \max_{x \in[a,b]} |f'''(x)| $
$$h= \text{step size}$$
$f'''$ stands for 3rd derivative
Let me know if I missed anything or if further clarification is needed. I kindly request you to review my proposed solution and provide feedback on its accuracy.
My Solution:
