Write a MATLAB user-defined function that determines the first and second derivatives of a function that is given by a set of discrete points with equal spacing. For the function name use [yd, ydd] = FrstScndDeriv (x, y). The input arguments x and y are vectors with the coordinates of the points, and the output arguments yd and ydd are vectors with the values of the first and second derivatives, respectively, at each point. For calculating both derivatives, the function should use the finite difference formulas that have a truncation error of O(h2 ).

(a) Use the function FrstScndDeri v to calculate the derivatives of the function that is given by the data in Problem 8.18.

(b) Modify the function (rename it FrstScndDeri vPt) such that it also creates three plots (one page in a column). The top plot should be of the function, the second plot of the first derivative, and the third of the second derivative. Apply the function Frst ScndDeri vPt to the data in Problem 8.18.

Problem

Write a MATLAB user-defined function that calculates the second derivative of a function that is given by a set of discrete data points with equal spacing. For the function name and arguments use ydd=SecDeriv (x, y), where the input arguments x and y are vectors with the coordinates of the points, and ydd is a vector with the values of the second derivative at each point. For calculating the second derivative, the function Sec Der iv should use the finite difference formulas that have a truncation error of O(h2 ). Use SecDeri v for calculating the second derivative of the function that is given by the following set of points: