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প্রদত্ত ফাংশন যেখানে x ∈ নিম্নলিখিত দুটি বিবৃতি বিবেচনা করুন:

(I) অন্তরালে f ক্রমবর্ধমান

(II) অন্তরালে f' ক্রমহ্রাসমান

উপরোক্ত দুটি বিবৃতির মধ্যে,

  1. শুধুমাত্র (I) সত্য।
  2. শুধুমাত্র (II) সত্য।
  3. (I) এবং (II) কোনটিই সত্য নয়।
  4. (I) এবং (II) উভয়ই সত্য।

Answer (Detailed Solution Below)

Option 1 : শুধুমাত্র (I) সত্য।

Detailed Solution

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গণনা:

প্রদত্ত,

⇒ 0 \quad f(x) \uparrow\)

⇒

⇒

∴ অন্তরালে f ক্রমবর্ধমান।

সঠিক উত্তর হল বিকল্প 1।

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