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Pure 2 coursework Decimal Search Method In order to find the root of the function f(x)=3x3-7x2-11x+17, the decimal search method was used. This is the process whereby a table of values is constructed that show whether the value of f(x) with certain values of x is positive or negative. By zooming in on the places where the value of f(x) switches from positive to negative (or vice versa), values for the root of this function can be found. x f(x) -4 -243 -3 -94 -2 -13 -1 18 0 17 1 2 2 -9 3 2 4 53 5 162 From this table, it is clear that there are roots where f(x)=0 when values of x lie between -2 and -1, 1 and 2, and 2 and 3. By concentrating on the interval of [1,2], the rot can be found to a greater level of accuracy. x f(x) 1 2 1.1 0.423 1.2 -1.096 1.3 -2.539 1.4 -3.888 1.5 -5.125 1.6 -6.232 1.7 -7.191 1.8 -7.984 1.9 -8.593 2 -9 It is now clear that the root lies somewhere inside the interval of [1.1, 1.2] x f(x) 1.1 0.423 1.11 0.268193 1.12 0.113984 1.13 -0.03961 1.14 -0.19257 1.15 -0.34488 1.16 -0.49651 1.17 -0.64746 1.18 -0.7977 1.19 -0.94722 1.2 -1.096 The root is in the interval [1.12, 1.13] x f(x) 1.12 0.113984 1.121 0.098597 1.122 0.083216 1.123 0.067841 1.124 0.052472 1.125 0.037109 1.126 0.021753 1.127 0.006403 1.128 -0.00894 1.129 -0.02428 1.13 -0.03961 The root is somewhere inside the interval [1.127, 1.128]....

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