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I thought to determine the function first but5 since only one information is given and according to that f(x) has one root alpha and at that point, the derivative has to be zero. So I tried to assume the function as y=x^2 but next, I faced problem in the greatest integer function while evaluating the limit. Any help would be appreciated.

Greatest Integer Function [X] indicates an integral part of the real number x which is nearest and smaller integer to x. It is also known as floor of X .

[x]=the largest integer that is less than or equal to x.

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    $\begingroup$ If $f(\alpha)^2 + f'(\alpha)^2 = 0$, then surely you must be working in the complex plane.... To this I would assume that $\dfrac{f(\alpha)}{f'(\alpha)} = i$. $\endgroup$ – JacobCheverie Apr 24 at 17:28

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