10.1.2 Change of Sign Failure

When can the sign change method fail?

• There are certain circumstances where achange of signfails to appropriately reflect the number or existence of roots
• If the interval istoo largethere may be more than one root within it
  • An偶数根smean roots are missed entirely as a sign change is not identified
  • Anodd number of roots ( > 1 )may mean not ALL roots are identified

• In adiscontinuousa sign change may occur which is not caused by a root but by anasymptote
• If a function接触到轴but does not pass through it there would be a root but no sign change