For the quartic

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

Problem

For the quartic

h_k(x)=x^{4}-4kx^{2}+k^{2}

, let

k

be real. Which of the following describes all values of

k

for which

h_k

possesses exactly one relative extremum? (a)

k=0

(b)

k<0

(c)

k\le 0

(d)

k>0