Figure 2: The bisection method selects the right subinterval. The root is to the right of x=c and f(c) f(b) < 0. EXAMPLE 1. Consider the continuous function f(x) = x3 + x â&#x20AC;&#x201C; 1. (a) Evaluate f(0). (b) Evaluate f(1). (c) Determine the sign of f(0) f(1). (d) What conclusion can you draw from (c)? (e) Use the bisection method to obtain the root of y = f(x) to four decimal places. SOLUTION TO EXAMPLE 1. (a) f(0) = -1 (b) f(1) = 1 (c) f(0) f(1) = (-1) Ă&#x2014; (1) = -1 < 0, i.e., the sign of f(0) f(1) is negative. (d) 0 < xroot < 1 (e) a 0 0.5 0.5 0.625 0.625 0.6563 0.6719 0.6797 0.6797
b 1 1 0.75 0.75 0.6875 0.6875 0.6875 0.6875 0.6836
2016 MAV Annual Conference Proceedings
a+b 2
0.5 0.75 0.625 0.6875 0.6563 0.6719 0.6797 0.6836 0.6817
f(a) -1 -0.375 -0.375 -0.1309 -0.1309 -0.0610 -0.0248 -0.0063 -0.0063
f(b) 1 1 0.1719 0.1719 0.0125 0.0125 0.0125 0.0125 0.0031
f( a+2 b ) -0.375 0.1719 -0.1309 0.0125 -0.0610 -0.0248 -0.0063 0.0031 -0.0015
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