Consider the experimental data below for a certain function: \begin{array}{c|cccccc}

x & 0 & 1 & 2 & 3 & 4 & 5 \\

\hline & & & & & & \\

f(x) & 2.1 & 7.7 & 13.6 & 27.2 & 40.9 & 61.1

\end{array} Show (do not formulate) that the set of normal equations to be solved to construct a quadratic least squares polynomial P(x) = ao + a₁x + a₂x² is given by

Given that the coefficients of the quadratic least squares polynomial in (a) above are ao = 2.4786, a₁ = (3)2.3593, a2 = 1.8607, write down the P(x) and use it to approximate ƒ(2.5). :) By selecting three suitable data points in the given set, construct a second degree Newton's divided (7)difference polynomial that interpolates the three selected points, and use it to find an approximation ofƒ(2.5). ) Approximate the value of f(2.5) using the least squares exponential form y = aoea¹. Compute the error in the approximation.