Virtual Labs

Given n+1 data pairs, a unique polynomials of degree _____________ passes through the n+1 data points.

a: n Explanation

Explanation

b: n+1 Explanation

Explanation

c: n+1 or less Explanation

Explanation

d: n or less Explanation

Explanation

Given the two points [a, f(a)], [b, f(b)], the linear Lagrange polynomial f₁x that passes through these two points is given by

f_1(x) = \frac{x-b}{a-b} f(a) + \frac{x-a}{a-b} f(b)

Explanation

f_1(x) = \frac{x}{b-a} f(a) + \frac{x}{b-a} f(b)

Explanation

f_1(x) = \frac{x-b}{a-b} f(a) + \frac{x-a}{b-a} f(b)

Explanation

f_1(x) = f(a) + \frac{f(b)-f(a)}{b-a} f(b-a)

Explanation

Differentiation - Method Based on Interpolation (Lagrange's Method)