




Solve f(x) = x^{3} 3x +1
We start at a = 0, b = 1.
f(1/2) < 0, b = 1/2 x =.0u
in binary notation;
u means unknown.
f(1/4) > 0, a = 1/4 x = .01u
f(3/8) < 0, b = 3/8 x = .010u
f(5/16) > 0, a = 5/16 x= .0101u
Notice that each evaluation determines one binary bit in the binary expression for the solution;
Thus, ten decimal place accuracy in this case requires thirty evaluations; since 2^{30} is near 10 ^{ 10} and b  a started at 1.