Q8Advanced Engineering Mathematics

When attempting to find an unknown independent variable $x$ for a specifically given dependent variable $y=10$, we forcefully swap their mathematical roles and utilize the Inverse Lagrange Interpolation formula: $x=\sum x_i\prod \frac{y-y_j}{y_i-y_j}$. Substituting all provided numerical coordinates into this polynomial and executing the arithmetic yields the highly accurate interpolated approximation $x\approx 16.466$.