Given that f(2)=4,f(2.5)=5.5 obtain the linear interpolation polynomial using Newton's Divided Difference
Newton's divided difference table is:
Newton's divided difference interpolation formula is:
f(x)=y0+(x−x0)f[x0,x1]f(x)=4+(x−2)×3f(x)=4+(3x−6)f(x)=3x−2f(x)=y_0+(x-x_0)f[x_0,x_1]\\f(x)=4+(x-2)\times 3\\f(x)=4+(3x-6)\\f(x)=3x-2f(x)=y0+(x−x0)f[x0,x1]f(x)=4+(x−2)×3f(x)=4+(3x−6)f(x)=3x−2
Answer:
Polynomial: y = 3x-2
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