ধরুন ফাংশন f(x) = xn , n ≠ 0 সমস্ত x এর জন্য পার্থক্যমূলক। তাহলে n ব্যবধানের যেকোনো উপাদান কত হতে পারে?

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NDA (Held On: 23 April 2017) Maths Previous Year paper
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  1. [1, ∞)
  2. (0, ∞)
  3. \(\left( {\frac{1}{2},{\rm{\;}}\infty } \right)\)
  4. উপরের কোনওটিই না

Answer (Detailed Solution Below)

Option 1 : [1, ∞)
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গণনা:

প্রদত্ত: f(x) = xn, n ≠ 0।

F'(x) = nxn – 1

f(x) পার্থক্যমূলক হওয়ার জন্য, n – 1 ≥ 0

সুতরাং, n ≥ 1.

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