# Given that Domain of the rational function is all real numbers. So the rational function should not contain denominator part.

Question
Rational functions
Given that Domain of the rational function is all real numbers.
So the rational function should not contain denominator part.

2020-11-06
So the required rational function only contains numerator part.
The required rational function is in the form of
$$f(x)=Kx(x-a)(x-b)$$
where k, a, and b are constants.

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My answer. The intervals do match and equal zero so Rolles theorem can work.
Second I found the derivative maybe thats where I can't solve this problem.
The derivative that I got was $$\displaystyle{64}-{x}^{{2}}+\frac{{x}}{\sqrt{{{64}-{x}^{{2}}}}}$$ maybe i did wrong on the simplifying. I at least tried hopefully some one can explain as much as possible with every single step because I can figure out the algebra part.
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