CIE A Level Maths: Pure 3复习笔记6.1.2 Change of Sign Failure

When can the sign change method fail?

• There are certain circumstances where a change of sign fails to appropriately reflect the number or existence of roots
• If the interval is too large there may be more than one root within it
  • An even number of roots mean roots are missed entirely as a sign change is not identified
  • An odd number of roots ( > 1 ) may mean not ALL roots are identified
• In a discontinuous a sign change may occur which is not caused by a root but by an asymptote
• If a function touches the x-axis but does not pass through it there would be a root but no sign change