Question

Using the X and Y values below, write a MATLAB function SECOND_DERIV in MATLAB. The output of the function should be the approximate value for the second derivative of the data at x, the input variable of the function.
Use the forward difference method and interpolate to get your final answer.
X=[1,1.2,1.44,1.73,2.07,2.49,2.99,3.58,4.3,5.16,6.19,7.43,8.92,10.7,12.84,15.41,18.49];
Y=[18.89,19.25,19.83,20.71,21.96,23.6,25.56,27.52,28.67,27.2,19.38,-2.05,-50.9,-152.82,-354.73,-741.48,-1465.11];

Answer 1

function second_Derivative = SECOND_DERIV(x)
X=[1,1.2,1.44,1.73,2.07,2.49,2.99,3.58,4.3,5.16,6.19,7.43,8.92,10.7,12.84,15.41,18.49];
Y=[18.89,19.25,19.83,20.71,21.96,23.6,25.56,27.52,28.67,27.2,19.38,-2.05,-50.9,-152.82,-354.73,-741.48,-1465.11];

dydx=diff(Y)./diff(X);%first derivative using forward difference
dy2dx2=diff(dydx)./diff(X(1:end-1));%second derivative using forward difference
X=X(1:end-2);%x values coresponding to 2nd derivatives in dyy
second_Derivative= interp1(X,dy2dx2,x,'linear','extrap');%using interpolation to find the second derivation at any point
%using extrap in case input x is beyond the range of X