Numerical Methods : Key Stage 5 (A2-Level) : Mathematics Content Knowledge
Key Stage 5 (A2-Level)
Question 1 of 3
1. How confident are you that you can locate:
a. roots by considering change of sign of f(x)?
If f(x) is continuous between x = a and x = b and the sign of f(x) changes between x = a and x = b then a root of f(x) exists between a and b.
For example, in the diagram above f(a) > 0 and f(b) < 0 so a root lies between a and b.
Show that a root of lies between x = 1 and x = 2.
The sign changes between x = 1 and x = 2 and therefore you will find a solution to f(x) = 0 between those two points.
Once you have found the bounds of a root you can use a decimal search or a binary search to find the actual value of the root to the required accuracy.
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