This is a MATLAB question it's really important it has 15 percent of my math grade.

Question. [15%) For the purpose of shrinking a trunnion into a hub, the reduction of diameter D of a trunnion shaft by cooling it through a temperature change of AT is given by where D = original diameter (in), and = coefficient of thermal expansion at average temperature (in/in/F) The trunnion is cooled from 80F to -108F, giving the average temperature as -14F. The table of the coefficient of thermal expansion vs. tempera ture data is given in the table below Temperature T(F) 80 -60 160 260 340 Thermal Expansion Coefficient, (in/in/oF) 6.47 x 10-6 6.00 10-6 5.58 x 10-6 .72 x 10-6 3.58 10-6 2.45 x 10-6 Using MATLAB software answer the following parts of the question: (a) If the coefficient of thermal expansion needs to be calculated at the average temperature of -14F, determine the value of the coefficient of thermal e possible second and third order Lagrange polynomials expansion at T =-14 using the best (b) Find the relative approximate error for the second order Lagrange polynomial approximation