Mathematics

Problem

For

0<k<\sqrt{6}

, let

R(k)

be the region bounded by the curves

y=12-x^{2}

and

y=kx

, together with the

y

-axis and the vertical line

x=k

. Determine the value of

k

at which the area of

R(k)

is extremal, and state whether this extremum is a maximum or a minimum.