For , define by . Find all real values of for which is one-to-one on…

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

For

k\in\mathbb{R}

, define

f_k:\mathbb{R}\to\mathbb{R}

f_k(x)=kx^{3}+(k-1)x

. Find all real values of

k

for which

f_k

is one-to-one on

\mathbb{R}