Answer to Question #55518 in Quantitative Methods for JOSEPH

Question

3 If f(1) = 1, f(3) = 19, f(4) = 49 and f(5) = 101, find the Lagrange’s interpolation polynomial of f(x).

a. P(x)=x 3 −x 2 +1
b. P(x)=x 3 –3x 2 −5x–4
c. P(x)=x 3 –3x 2 +5x–6
d. P(x)=2x 2 –3x+5x–6
4 The first divided difference of f with respect to
x i
and
x i+1
denoted by
f[x i ,x i+1 ]
is defined as
a. f[x i ,x i+1 ]=f[x i+1 ]−f[x i ]x i+1 −x i
b. f[x i ,x i+1 ]=x i+1 −x i f[x i+1 ]−f[x i ]
c. f[x i ,x i+1 ]=f[x i ]−f[x i+1 ]x i+1 −x i
d. f[x i ,x i+1 ]=f[x i ]−f[x i+1 ]f[x i+1 ]−x i