Section

Lagrange polynomials of the manufactured bottle

S1

$P_1\left(x\right)=0.0\widehat{5}x+1.1$

S2

$P_2\left(x\right)=-0.020833333333335x^2+1.239583333333336x-1.945000000000007$

S3

$\begin{array}{c}{P}_3\left(x\right)=-0.005166029622552x^3-0.276176540850457x^2\\ +3.629662267080676x-7.090307990922156\end{array}$

S4

$\begin{array}{c}{P}_4\left(x\right)=0.053631553631554x^3-0.704280904280836x^2\\ +1.489891774891476x+8.776333333333241\end{array}$

S5

$P_5\left(x\right)=-0.702832244008714x^2+13.148997821350747x-57.474738562091602$

S6

$P_0\left(x\right)=3.915$

S7

$\begin{array}{c}{P}_6\left(x\right)=-0.0773358585859x^3+0.031823232323232x^2\\ -0.435284469696971x+2.018724999999995\end{array}$