Practice question · Fill in the blanks
Complete the precondition for bisection.
Bisection can be started only when f has ______ at the two endpoints of the interval.
Word bank: equal values · opposite signs · zero derivative · the same sign
Hints
- The method rests on the Intermediate Value Theorem.
- Which configuration forces a continuous function to cross zero?
Show the answer
Bisection can be started only when f has opposite signs at the two endpoints of the interval.
Why
Opposite signs at the endpoints force a continuous function to cross zero somewhere between them, which is the guarantee bisection exploits. With the same sign there may be no root, or an even number of them, and the method has nothing to bisect.
Practise Root Finding
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