Given the data Calculate f34 using Newtons interpolating pol

Given the data Calculate f(3.4) using Newton\'s interpolating polynomials of order 1 through 3.

Solution

v(t)=b0+b1(t-t0)

here

b0=v(t0)=8

v(t1)=2

v(t0)=8

t1=4

t0=3

t=3.4

then

b1=(v(t1)-v(t0))/(t1-t0)

b1= -6

then

v(t)=b0+b1(t-t0)

v(t)=8+(-6)(3.4-3)

v(t)= 5.6