<image>A pharmaceutical research institute has developed a new antibacterial drug. After years of animal testing, it is being used for the first time in clinical human trials. The relationship between the drug concentration in the blood $$y$$ (micrograms/milliliter) and the time after taking the drug $$x$$ (hours) is shown in the function graph below $$($$when $$4\leqslant x\leqslant 10$$, $$y$$ is inversely proportional to $$x$$).



$$(1)$$ Based on the graph, derive the functional relationship between $$y$$ and $$x$$ during both the increasing and decreasing stages of drug concentration in the blood.
$$(2)$$ How many hours does the drug concentration in the blood remain no less than $$4$$ micrograms/milliliter?