Let , where . Determine all real values of such that and simultaneously…

MATHEMATICS · Subjective · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Let

f(x)=k x^{3}+2x^{2}-5

, where

k\in\mathbb{R}

. Determine all real values of

k

such that

\displaystyle\lim_{x\to\infty}f(x)=-\infty

and simultaneously

\displaystyle\lim_{x\to -\infty}f(x)=+\infty