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The function f(x) = 2x3 – 3x2 – 36x + 2 has its maxima at
  • a)
    x = – 2 only
  • b)
    x = 0 only
  • c)
    x = 3 only
  • d)
    both x = – 2 and x = 3
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The function f(x) = 2x3 – 3x2 – 36x + 2 has its maxima ata)x = – 2 on...
For maximum f(x),
⇒ f'(x) = 0
⇒ 6x2−6x−36=0
⇒ x2−x−6=0
⇒ x2−3x+2x−6=0
⇒ x(x-3)+2(x-3)=0
⇒ x = 3, -2
∴ f''(x) = 12x-6
⇒ f''(x)<0 @x="">
So, f(x) has a maximum value at -2 only.
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The function f(x) = 2x3 – 3x2 – 36x + 2 has its maxima ata)x = – 2 onlyb)x = 0 onlyc)x = 3 onlyd)both x = – 2 and x = 3Correct answer is option 'A'. Can you explain this answer?
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