'Change of Sign Method'

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MATHEMATICS COURSEWORK

Numerical Methods can be used to solve those equations which cannot be solved analytically.

One such method is the 'Change of Sign Method', focusing on Decimal Search.

Decimal search is based on the principal that f(x) changes sign as a curve passes through the x axis at a root.

Above the x axis, f(x) is positive and below the x axis f(x) is negative.

Using this principal, values of f(x) are initially found and consecutive values are found in increments of 0.1 until a change in sign is found. If further accuracy is required, consecutives values could then be found in increments of 0.01 and 0.001, until a change of accuracy is found, therefore giving one root of the equation.

EVIDENCE

Equation: y=0.6938x3 - 0.9157x2 - 1.421x + 1.671

GRAPH:

TABLE OF RESULTS

First Interval

x

f(x)

1

0.0281

1.1

-0.07665

1.2

-0.1539

1.3

-0.1996

1.4

-0.2094

1.5

-0.1792

1.6

-0.105

1.7

0.01757

1.8

0.1926

1.9

0.4242

The table shows that the sign