Answer to Question #189177 in Quantitative Methods for Kogosi Geoffry Jum

Question

Given that f(2)=4,f(2.5)=5.5 obtain the linear interpolation polynomial using Newton's Divided Difference

Answer 1

Newton's divided difference table is:

Newton's divided difference interpolation formula is:

$f(x)=y_0+(x-x_0)f[x_0,x_1]\\f(x)=4+(x-2)\times 3\\f(x)=4+(3x-6)\\f(x)=3x-2$

Answer:

Polynomial: y = 3x-2