Let f:(a,infinity)-->R (reals) be differentiable and let A and B be real numbers. Prove that if f(x)-->A and f '(x)-->B as x --> infinity, then B=0.(adsbygoogle = window.adsbygoogle || []).push({});

I would guess that the mean value theorem may be needed but I am not sure how to use it considering that we're dealing with x --> infinity.

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# Differentiability and convergence.

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