The function f(x) = x^3 - 5x^2 - 8x/3 is Option 1: positive and monotonically increasing for x (-∞, 5-sqrt(57)2) and x (5+sqrt(57)2, +∞) Option 2: negative and monotonically decreasing for x (-∞, 5-sqrt(57)2) and x (5+sqrt(57)2,+∞) Option 3: negative and monotonically increasing for x (-∞, 5-sqrt(57)2) and positive and monotonically increasing for x (5+sqrt(57)2,+∞) Option 4: positive and monotonically increasing for x (-∞, 5-sqrt(57)2) and negative and monotonically decreasing for x (5+sqrt(57)2,+∞)

The answer is 'negative and monotonically increasing for x (-∞, 5-sqrt(57)2) and positive and monotonically increasing for x (5+sqrt(57)2,+∞)'. View full solution:

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

IPMAT Indore

Algebra

Hard

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

IPMAT Indore (MCQ) PYQs

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