Failure of the Change of Sign Method (Edexcel IAL Maths)

Change of Sign Failure

Spec point — 6.1

Failure of the change of sign method

When can the change of sign 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 funciton, 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

Worked Example