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