Using Newton's forward difference formula, the cubic polynomial that can be fitted to the above data, is
A
2x3+7x2−6x+2
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B
2x3−7x2+6x−2
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C
x3−7x2−6x+1
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D
2x3−7x2+6x+1
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Solution
The correct option is D2x3−7x2+6x+1 The difference table for the given data
x
0
1
2
3
f(x)
1=f(0)
2
1
10
Δ2f(x)
1=Δf(0)
-1
9
Δ2f(x)
-2=Δ2f(0)
10
Δ3f(x)
12=Δ3f(0)
x0=0
Newton's forward difference formula
Diagram f(x)=1+x()+(x2−x2)(−2)+((x3−3x2+2x)6)×12 f(x)=1+x−x2+x+2x3−6x2+4x f(x)=2x3−7x2+6x+1
Note: In examination, the students are advised to check options by putting values of x.