For the given x_0=0, x1=1 and x2=2,

Question

1)Construct the quadratic Lagrange Interpolation Polinomial for f(x)=3^x
2)Find the error for each x€[0,2]

1) I found the quadratic Lagrange Interpolation Polinomial as,

y_(x)= (2*(x)^2) + 1

So y'(x)=4x
y''(x)=4
y'''(x)=0

I know the error bound(formula) for Lagrange Interpolation Polinomial is,

|error| <= [(1/(n+1)!]*| [(f^(n+1))(c)|*| ((pi) (i=0-->n)(x - x_i))|

Since y'''(x)=0, how do we find the error?

What is meant by find error each x€[0,2]?

Thank you

Answer 1

If Y"' = 0 then the error is zero.
In fact, at x = 0,1,2 the error is zero.
3^0 = 2*0^2 + 1
3^1 = 2*1^2 + 1
3^2 = 2*2^2 + 1

Answer 2

Thank you very much