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];

Matlab please

Answer 1

function secDer = 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];

%first derivative using forward difference   
dy=diff(Y)./diff(X);

%second derivative using forward difference
dyy=diff(dy);

%x values coresponding to 2nd derivatives in dyy
X=X(1:end-2);
%using interpolation to find the second derivation at any point
secDer= interp1(X,dyy,x,'linear','extrap');
%using extrap in case input x is beyond the range of X

- Function secDer = 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, 12.84,1 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,-5 Command Window >> SECOND_DERIV (1) ans = 0.6167 >> SECOND_DERIV (45) ans = -510.0902 >> SECOND_DERIV(-3) ans = 0.5937 HNM 1000 . first derivative using forward difference dy=diff(Y)./diff(x); second derivative using forward difference dyy=diff (dy); N $x values coresponding to 2nd derivatives in dyy X=X (1:end-2); fusing interpolation to find the second derivation at any point secDer= interpl (X, dyy, x, 'linear', 'extrap'); Susing extrap in case input x is beyond the range of X 15 -