IPMAT Indore 2019 (MCQ) - The function f(x) = x^3 - 5x^2 - 8x/3 is | PYQs + Solutions

IPMAT Indore 2019

Algebra

Functions

Hard

The function $f(x) = \dfrac{x^3 - 5x^2 - 8x}{3}$ is

positive and monotonically increasing for x

\in (-\infty, \frac{5-\sqrt{57}}{2})

and x

\in (\frac{5+\sqrt{57}}{2}, +\infty)

negative and monotonically decreasing for x

\in (-\infty, \frac{5-\sqrt{57}}{2})

and x

\in (\frac{5+\sqrt{57}}{2},+\infty)

negative and monotonically increasing for x

\in (-\infty, \frac{5-\sqrt{57}}{2})

and positive and monotonically increasing for x

\in (\frac{5+\sqrt{57}}{2},+\infty)

positive and monotonically increasing for x

\in (-\infty, \frac{5-\sqrt{57}}{2})

and negative and monotonically decreasing for x

\in (\frac{5+\sqrt{57}}{2},+\infty)

✅ Correct Option: 3