For the family of functions

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

Problem

h_k(x)=x^{3}-3kx^{2}

, determine the set of all real values of

k

for which

h_k

is increasing on the entire interval

(0,4)

. (a)

k<2

(b)

k\le 0

(c)

k<0

(d)

k>0