a) Type up and save the function “secant” below exactly as is and save it among

Question

a) Type up and save the function “secant” below exactly as is and save it among all your MATLAB work in your Mosaic account. Then type in this line in the main MATLAB command window (you will have to be in the same directory as the secant function):

root = secant (@(x) x^2+3x-1, 1, 0, 0.00001, 50)

Describe in your own words what you got here. When will this program stop the iterations? Name the two conditions specifically.

b) Now change the function in the line above from x^2+3x-1 to 35000-857x+40x^1.5. What solution did you get from this program? What solution did you get from your manual secant calculations? Are they the same? Why?

MATLAB:

function root = secant (func, xrold, xr, es, maxit)

if nargin<5, maxit=50; end

if nargin<4, es=0.001; end

iter=0;

while (1)

        xrn=xr-func(xr)*(xrold-xr)/(func(xrold)-func(xr));

        iter=iter+1;

        if xrn~=0, ea=abs((xrn-xr)/xrn)*100; end

        if ea<=es | iter >= maxit, break, end

        xrold=xr;

        xr=xrn;

end

root=xrn;

Explanation / Answer

(a)
The solution I got is 0.30278
The iterations stop when the 2 consecutive solutions we got have a difference less than or equal to 0.00001
or the maximum number of iterations is more than or equal to 50.

(b)
The solution I get is 65.690

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