Practice question · Sort into groups
Let f(x) = x cubed - x - 2. Sort each interval by whether bisection can be started on it.
Groups: Sign change: can start · No sign change
- 0 to 1
- 0 to 2
- 1 to 2
- 2 to 3
- minus 2 to 0
Hints
- Evaluate f at every endpoint mentioned before judging any interval.
- f(0) = -2, f(1) = -2, f(2) = 4 and f(3) = 22.
Show the answer
Sign change: can start: 1 to 2, 0 to 2
No sign change: 0 to 1, 2 to 3, minus 2 to 0
Why
f(-2) = -8, f(0) = -2, f(1) = -2, f(2) = 4, f(3) = 22, so only intervals with one endpoint at or beyond 2 and one below it change sign. The interval 0 to 1 has two negative values, so bisection has nothing to work with even though the function is perfectly well behaved there.
Practise Root Finding
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