Answer to Question #343209 in Quantitative Methods for Raju

Question #343209

Find Larange’s interpolating polynomial passing through set of points



(0,2) (2,-2),(3,-1),Use it to find





at x = 2


1
Expert's answer
2022-05-22T23:42:32-0400

Lagrange Second Order Interpolation Formula  can be written as


"f(x)=\\dfrac{(x-x_1)(x-x_2)}{(x_0-x_1)(x_0-x_2)}y_0"

"+\\dfrac{(x-x_0)(x-x_2)}{(x_1-x_0)(x_1-x_2)}y_1+\\dfrac{(x-x_0)(x-x_1)}{(x_2-x_0)(x_2-x_1)}y_2"

Substitute


"f(x)=\\dfrac{(x-2)(x-3)}{(0-2)(0-3)}(2)+\\dfrac{(x-0)(x-3)}{(2-0)(2-3)}(-2)"

"+\\dfrac{(x-0)(x-2)}{(3-0)(3-2)}(-1)"

"=\\dfrac{1}{3}x^2-\\dfrac{5}{3}x+2+x^2-3x-\\dfrac{1}{3}x^2+\\dfrac{2}{3}x"

"f(x)=x^2-4x+2"


"f(2)=(2)^2-4(2)+2=-2"


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