যদি ফাংশন f(x) = x2 - kx ব্যবধানে একঘেয়েভাবে বৃদ্ধি পায় (1, ∞), তাহলে নীচের কোনটি সঠিক?

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

Answer (Detailed Solution Below)

Option 1 : k < 2
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Detailed Solution

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অনুসৃত সূত্র:

পার্থক্য সূত্র:

গণনা:

f(x) = x2 - kx

⇒ f ' (x) = 2x - k

যেহেতু, f একঘেয়েভাবে বাড়ছে।

f ' (x) > 0

⇒ 2x - k > 0

⇒ k

যেহেতু, আমাদের 1

⇒ 2

(1) এবং (2) থেকে পাই,

k

∴ সঠিক সম্পর্কটি হল k

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