Age 16 to 18 Challenge Level:
As a hint, try comparing the '$7$'s' inequality to a similar one
for $8$. For the '$4$'s' inequality use the fact that any root of
$4$ is greater than $1$.
To sketch the graph, find the derivative for $x=0$ and then
consider where the derivative is positive, where it is negative and
if it tends to a limit as $x$ increases.