Consider the function

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

f_k(x)=x^{3}+3kx^{2}+5

, where

k\in\mathbb{R}

. For which value(s) of

k

f_k

increasing on the entire real line? (a)

k>0

(b) \text{all real }k (c)

k=0

(d)

k<0