For a function /, the Newton divided-difference formula gives the interpolating polynomial P3(x) = 1 + 4x + 4x(x - 0.25) + yxU - 0.25)(x - 0.5), on the nodes xq = 0, x, = 0.25, X2 = 0.5 and xj = 0.75. Find /(0.75)

Step 1 of 2

For a function f, the Newton divided difference formula gives the interpolating polynomial

To find .

The constant term is 1. Therefore,

Now, let us take . It gives,

The coefficient of is 4. Then,

Proceeding in this manner,