1. Create a function-function that uses the incremental search algorithm to find root brackets without using a for loop. In other words, vectorize your incremental search function. The inputs and outputs are the same as the code in Fig. 5.4 of your text (you can omit the input checking and bracket number display code). The first line of your code is as follows: function xb = incsearchv(func,xmin,xmax,ns)

FIG. 5.4:

function xb = incsearch(func,xmin,xmax,ns) % incsearch: incremental search root locator 

% xb = incsearch(func,xmin,xmax,ns): % finds brackets of x that contain sign changes % of a function on an interval % input: % func = name of function % xmin, xmax = endpoints of interval % ns = number of subintervals (default = 50) % output: % xb(k,1) is the lower bound of the kth sign change % xb(k,2) is the upper bound of the kth sign change % If no brackets found, xb = []. 

if nargin < 3, error('at least 3 arguments required'), end if nargin < 4, ns = 50; end %if ns blank set to 50 

% Incremental search x = linspace(xmin,xmax,ns); f = func(x); nb = 0; xb = []; %xb is null unless sign change detected for k = 1:length(x)1 

if sign(f(k)) ~= sign(f(k+1)) %check for sign change

nb = nb + 1; xb(nb,1) = x(k); xb(nb,2) = x(k+1);

end

end

if isempty(xb) %display that no brackets were found disp('no brackets found') disp('check interval or increase ns') 

else disp('number of brackets:') %display number of brackets disp(nb) 

end