how to find arrange the following functions in increasing or decreasing order? I have the following three functions
$f_1(x) = \frac{1}{4}  (8-3x + \sqrt{(x-2) (5x-14)}) (1-x)$
$f_2(x) = \frac{1}{8} (12-4x + \sqrt{2} \sqrt{(5x-14)(x-3)} + \sqrt{2} \sqrt{(x-2)(x-3)} )(1-x)$
$f_3(x) = (x-1)(x-2)$
How possible can it be shown that
$f_1(x) > (or <)  f_2(x) < (or >) f_3(x)$

If you are interested as $x \to \infty$, you can just look for the highest power of $x$.  For $f_1(x)$, the square root goes as $\sqrt 5x$, so the whole thing goes as $(3-\sqrt 5)x^2$.  You can do similarly with the second and the third is $x^2$.  This says that as $x \to \infty, f_3(x) \gt f_1(x)$
If you are interested in all $x$, note that they all are $0$ at $x=1$, so none is strictly greater than any other.
