%Program 1.1 Bisection Method
%Computes approximate solution of f(x)=0
%Input: inline function f; a,b such that f(a)*f(b)<0,
% and tolerance tol
%Output: Approximate solution xc
function xc = bisect(f,a,b,tol)
if sign(f(a))*sign(f(b)) >= 0
error('f(a)f(b)<0 not satisfied!') %ceases execution
end
fa=f(a);
fb=f(b);
k = 0;
while (b-a)/2>tol
c=(a+b)/2;
fc=f(c);
if fc == 0 %c is a solution, done
break
end
if sign(fc)*sign(fa)<0 %a and c make the new interval
b=c;fb=fc;
else %c and b make the new interval
a=c;fa=fc;
end
end
xc=(a+b)/2; %new midpoint is best estimate
The following input discovers the first root for this graph.

>> f = @(t) F_project1(t);
>> bisect(f,-.8,-.7,1e^-10);

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