Consider the family of regions ,

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Consider the family of regions

S(k)

0 < k < 3

, each bounded above by

y = 9 - x^2

, below by

y = kx

, and between

x = 0

and

x = k

. For which value of

k

does the area of

S(k)

attain its maximum? (a)

k=\dfrac{3}{\sqrt{2}}

(b)

k=\sqrt{\dfrac{6}{5}}

(c)

k=\sqrt{\dfrac{18}{5}}

(d)

k=\sqrt{\dfrac{9}{5}}