How do we use Rolle's theorem to prove that there is at most one solution of in [-1,1] for any b and for what values of b does this have a solution in [-1,1]?
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If were roots of then, would exist such that , but (contradiction). Try the second question. Fernando Revilla
Originally Posted by maximus101 How do we use Rolle's theorem to prove that there is at most one solution of in [-1,1] for any b Let in the interval . So f(x) is decreasing in the interval . Therefore, there is at most one solution of in for any . PS: This method does not use Rolle's theorem, though.
Last edited by alexmahone; February 11th 2011 at 06:18 AM. Reason: Added postscript
Originally Posted by maximus101 and for what values of b does this have a solution in [-1,1]? For the conditions of the intermediate value theorem to be satisfied, and should have opposite signs. (Note that f is a decreasing function.)
Last edited by alexmahone; February 11th 2011 at 06:42 AM. Reason: Stupid mistake
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