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x এর মান নির্ণয় করুন যার জন্য f(x) = x - e x একটি ক্রমবর্ধমান ফাংশন হবে?

  1. (0, ∞)
  2. [0, ∞)
  3. (-∞, 0)
  4. উপরের কোনোটিই নয়

Answer (Detailed Solution Below)

Option 3 : (-∞, 0)
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Detailed Solution

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অনুসৃত ধারণা:

  • যদি f′(x) > 0 তাহলে ফাংশনটি বৃদ্ধি পাচ্ছে বলে বলা হয়।
  • যদি f′(x) <0 হয় তাহলে ফাংশনটি হ্রাস পাচ্ছে বলা হয়।

গণনা:

প্রদত্ত:

f(x) = x - ex

x এর সাথে পার্থক্য করে, আমরা পাই

⇒ f'(x) = 1 - ex

ফাংশন বাড়ানোর জন্য,

f'(x) > 0

⇒ 1 – ex > 0

⇒ ex < 1

⇒ ex < e0

∴ x < 0

সুতরাং, x ∈ (-∞, 0)

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