Mathematics

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.