$(10$ pts$)$ An experiment is performed to define the relationship between applied stress and

the time to fracture for a type of stainless steel. Eight different values of stress are applied,

and the resulting data are

Plot these data in Matlab and then develop a fitting equation to predict the fracture time for an

applied stress of $23k\frac{g}{m}{m}^2$ using the following methods.

i$.(5$ pts$)$ Quadratic Lagrangian Polynomial Interpolation Method $($solve by

hand$)$

ii$.(5$ pts$)$ Quadratic Newton Divided Difference Polynomial Interpolation

Method$($solve by hand$)$