Question

x	6.95	11	15.05	19.10	23.15	27.20	31.25	35.30
y	38	48.17	57.13	63.83	67.47	67.63	64.28	57.82

Use central-difference formulae of O(h4) to calculate the first and second derivatives at x = 15.05. Also provide the equation of the tangent line at that datum. Use the full accuracy of your calculator for all calculations, but provide all final answers with four decimal places

Answer 1

Central-difference formula for first derivative is ,

At   

and

Central-difference formula for second derivative

Substituting the values of and