Give an example of a function for which the bisection method DOES NOT converge l

Question

Give an example of a function for which the bisection method DOES NOT converge linearly.

That is, a function where en <= c*en-1 for ALL n, where c<=1. So on starting interval [a,b], the error e1=r-b, (where r is the actual root of the function) then after doing bisection method and getting the midpoint (x2) has error e2=r-x2. Now this e2 must be greater than e1 for all en. I have tried numerous functions, and the bisection method seems to always produce an error which is smaller than the previous error, rather than bigger. I just need one example where this is NOT true. Thank you.

Explanation / Answer

Check out this link :

http://www.chegg.com/homework-help/give-example-function-bisection-method-converge-linearly-chapter-3.1-problem-5p-solution-9780495114758-exc

I hope it will help you :)

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