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Pure 2 Coursework Task I) Systematic search for a change of sign. We are looking for solutions to f (x)=0, i.e. where the curve crosses the x-axis. The first thing to do is to draw a graph. For this method, initial boundary values are needed, and a graph is a good way to do this, and to check that the particular equation can be solved using this method. It is convenient if the boundary values c & d are a whole unit apart e.g. 2 and 3.It will be noted that c and d have opposite signs, in this example c is -ve and d +ve. Now, you have to calculate f (x) for x, which is incremented in steps of 0.1 from c to d. The resulting table might look like this: Decimal Search X = c + 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 f(x) -ve -ve -ve -ve -ve -ve -ve +ve +ve +ve +ve We now know that the root we are looking for lies...

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