_{Hello, out there! I am Samuel. Please, I need your assistance to fit the following set of data points with a polynomial (could be Newtons divided difference polynomial): }

i 0 1 2 3 4 5 6 7 8 9 01 11 xi 0.005 0.01 0.02 0.03 0.05 0.1 0.2 0.3 0.4 0.6 0.8 1.0 f(xi) 0.376 0.41 0.428 0.486 0.537 0.624 0.556 0.512 0.450 0.378 0.274 0.106 _{ I need the polynomial to pass through all the data points. Looking forward to your kind response. Thanks. }