Sign change
Intermediate Value Theorem.
Method. Evaluate at endpoints of interval. If (or vice versa), and is continuous, then root exists in .
Mathematical statement. Intermediate Value Theorem.
Example. .
- .
- .
- is polynomial β continuous.
- β΄ root exists in .
Cambridge tip. Always state continuity (or 'polynomial, hence continuous'). Mark scheme requires it.
- Compute and .
- Sign change + continuity β root.
- State continuity explicitly.
See the full worked example for numerical solution of equations β