For the function

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

Problem

For the function

f_k(x)=x^{4}+2k x^{3}

, with real parameter

k

f_k'(0)=f_k''(0)=0

. For which value of

k

x=0

a local minimum? (a)

k=2

(b)

k=-1

(c)

k=0

(d) Every non-zero real

k