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 f(x) = x3 + x2 + kx 

కి స్థానిక శీర్షాలు లేని పరిస్థితి ఏమిటి?

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  1. 4k < 1
  2. 3k > 1
  3. 3k < 1
  4. 3k ≤ 1

Answer (Detailed Solution Below)

Option 2 : 3k > 1
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Detailed Solution

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ఉపయోగించిన ఫార్ములా:

గణన:

f(x) = x3 + x2 + kx

f'(x) = 3x2 + 2x + k

శీర్షాలు లేకుండా, f తప్పనిసరిగా సున్నా మలుపులను కలిగి ఉండాలి, అంటే పైన ఉన్న చతురస్రాకారానికి అసలు మూలం లేదు.

22 - 4 × 3 × k

4 - 12k

4

1

3k > 1

∴ f(x) = x3 + x2 + kxకి స్థానిక శీర్షం 3k > 1 లేదు అనే షరతు

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