Question

First Derivative Central:

Write a user written function that expects as its input argument a vector of x values and a vector of corresponding y-values. The function must return a matrix with 2 columns. The first column contains ‘mid-point’ x-values. The second column must contain the centered difference approximations for the first derivative, dy/dx, at the step midpoints. In other words, the x values [(x2+ x1) / 2 , (x3+ x2) / 2,..., (xn+ xn-1) / 2] and corresponding first derivatives estimates should be returned.

Must be completed using loops, if/else statements and indexing in matlab. Cannot use matlab functions to solve for the derivatives. The x and y vector values are random and not given.

Answer 1

Mat lab Program:

clear
clc
% taking x and as a random vector
x=input('Enter the vector of x: ');
% use this as input [0 1 2 3 4 5 6 7 8 9 10];
y=input('Enter the vector of y: ');
% use this as input [0 1 4 9 16 25 36 49 64 81 100];
i=1;
if length(x)~=length(y)
error('Enter both the vectors of same length');
end
n=length(x);
X=zeros(n-1,1);
Y=zeros(n-1,1);
for i=1:n-1
% X is mean of the vector X
X(i)=(x(i)+x(i+1))/2;
% Y is central difference
Y(i)=((y(i+1)-y(i))/(x(i+1)-x(i)));
end
disp([X Y]);

Screenshot:

Save the above program and execute it.

Give the input.

Result:

Note: the function I used is x^2

So, the derivative is 2*x, and the answer is matching.

I hope this will help you, please give me thumbs-up.