Q1Advanced Engineering Mathematics I

Question

From the following table find $f^{'} (6)$ : | x | 0 | 2 | 3 | 4 | 7 | 9 | |---|---|---|---|---|---|---| | f(x) | 4 | 26 | 58 | 112 | 466 | 922 |

Answer 1

To find $f^{'} (6)$ , which is a point not exactly at the beginning or end of the table, we can use a central difference formula (like Stirling's or Bessel's) or interpolate a polynomial using Newton's Divided Difference formula (since the intervals are unequal: 0, 2, 3, 4, 7, 9) and then differentiate the polynomial.

Construct a Divided Difference Table, write out the Newton polynomial, differentiate it with respect to $x$ , and substitute $x = 6$ .

Q1Advanced Engineering Mathematics I

Question

Answer