Thread: Existence of a root

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

Originally Posted by NonCommAlg

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

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