Problem

Consider the function

f(x)=\sqrt{x^2\ln x+4-x^2}

, where

x\in\mathbb{R}

x>0

. a. Show that the distance,

l

, between the origin and any point on the graph of

f

is given by

l=\sqrt{x^2\ln x+4}

. b. Hence, find the

x

-coordinate of the point on the graph of

f

which is closest to the origin.