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Let $f(x)=\cfrac{5}{x}$. If the rate of change at $x=c$ is four times its rate of change at $x=3$, then $c=\underline{\hspace{2cm}}$.

$\cfrac{3}{4}$

$\pm 2 \sqrt{3}$

$\pm \cfrac{9}{4}$

$\pm \cfrac{3}{2}$