Topic explanation

Standard explanation

For continuous f, opposite signs at a and b guarantee at least one root in (a,b).

Key points

• Sign change and root bracketing
• rule
• worked example
• Sign change and root bracketing: For continuous f, opposite signs at a and b guarantee at least one root in (a,b).
• CONCEPT AND RULE: For continuous f, opposite signs at a and b guarantee at least one root in (a,b).
• METHOD: For sign change and root bracketing, identify the given information and required result. Select the
• For continuous f, opposite signs at a and b guarantee at least one root in (a,b).
• Worked pattern: f(x)=x^2-2 changes sign between 1 and 2.

Labelled diagram