Consider the polynomial P2(x) of degree 2 interpolating the function f(x) = cos(x) on the interval...

Transcribed Image Text:

Consider the polynomial P2(x) of degree 2 interpolating the function f(x) = cos(x) on the interval [0, π/3] at the points x = 0, x1 = π/4, and x2 = 7/3. Estimate the maximum of the interpolation absolute error for x = [0, π/3], i.e., give an upper bound for this absolute error max cos(x) - P₂(x)| ≤? TE[0,π/3] Remark: you are not asked to give the interpolation polynomial P₂(x). Consider the polynomial P2(x) of degree 2 interpolating the function f(x) = cos(x) on the interval [0, π/3] at the points x = 0, x1 = π/4, and x2 = 7/3. Estimate the maximum of the interpolation absolute error for x = [0, π/3], i.e., give an upper bound for this absolute error max cos(x) - P₂(x)| ≤? TE[0,π/3] Remark: you are not asked to give the interpolation polynomial P₂(x).