Question

Using finite differences, show that the data

x − 3 − 2 −1 0 1 2 3
f (x) 13 7 3 1 1 3 7
represents a second degree polynomial. Obtain this polynomial using interpolation
and find f(5.2) .

Answer 1

Question #46686, Math / Other

Using finite differences, show that the data

x-3-2-10123

f(x) 13731137

represents a second degree polynomial. Obtain this polynomial using interpolation

and find )5.2(f .

Answer.

The second differences are constant so the data represents a second degree polynomial.

$$f (x) = a x ^ {2} + b x + c$$ $$f (0) = 1 \rightarrow c = 1;$$ $$f(1) = 1 \rightarrow a + b + 1 = 1 \rightarrow b = -a;$$ $$f(-1) = 3 \rightarrow a \mp a + 1 = 3 \rightarrow a = 1.$$

Finally: $f(x) = x^{2} - x + 1$.

$$f(5.2) = 5.2^{2} - 5.2 + 1 = 22.84.$$

Answer provided by https://www.AssignmentExpert.com