Let [itex]f:[a,b] \rightarrow R[/itex] be a continuous function such that [itex]f(a)=f(b)=0[/itex] and [itex]f'[/itex] exists on [itex](a,b)[/itex]. Prove that for every real [itex]\lambda[/itex] there is a [itex] c \in (a,b)[/itex] such that [itex]f'(c) = \lambda f(c)[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

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# Real Analysis / Advanced Calc Puzzler

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