Let where is a real parameter

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

Problem

Let

f_k(x)=x^{3}-3kx

where

k

is a real parameter. Which of the following conditions on

k

is both necessary and sufficient for

f_k

to possess one relative maximum and one relative minimum? (a)

k\ne 0

(b)

k>0

(c)

k\ge 0

(d)

k>1