Question

The function f(x) satisfies f(5) = 29, and f(7) = 47. Let P(x) be LAGRANGE interpolation polynomial of degree 1 which passes through the given points on the graph of f(x). Make formula of P1

Answer 1

Hi,

Explanation:

`Points\ (5,29),(7,47)\\\\l_0(X)=(X-7)/(5-7) =(-x+7)/(2) \\\\l_1(X)=(X-5)/(7-5) =(x-5)/(2) \\\\P_1(X)=29*(-x+7)/(2)+47*(x-5)/(2)=\boxed{9X-11}`