We have two functions such that is continuous, is decreasing, and Prove that there exists such that

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- Sep 8th 2009, 07:00 PMNonCommAlgExistence of a root
We have two functions such that is continuous, is decreasing, and Prove that there exists such that

- Sep 8th 2009, 11:08 PMCaptainBlack
Binary search will converge to a point such that for all (that is for all small enough):

and

Thus either or there is an increasing jump discontinuity at . But an increasing jump at c is imposible given that g(x) is continuous and f(x)+g(x) and decreasing at c.

CB