if f(x)=x^3; show that f(a,b,c)=a+b+c
 

This question is from second order divided difference.

it goes as follows

we have

f(x)=x^3

for first divided difference

f(a,b) = {f(b)-f(a)}/(b-a)

= {b^3-a^3}/(b-a)

= a^2-ab+b^2

similarly
f(b,c) = b^2-bc+c^2

now the second divided difference will be

f(a,b,c) = {f(b,c)-f(a,b)}/(c-a)

solving we get

= a+b+c

thus

f(a,b,c) = a+b+c