Consider the function

MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

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

, where

x\in\mathbb{R}

and

x>0

. (1) 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}

. (2) Hence, find the

x

-coordinate of the point on the graph of

f

that is closest to the origin.